import Pretty.Defs.Resolve
import Pretty.Supports.MeasRender
import Pretty.Supports.ResolvePareto
import Pretty.Supports.ResolveOptimality
import Pretty.Claims.Widen

/-!
## Optimality theorems
-/

mutual
  /--
  The optimality theorem (Theorem 5.7)
  -/
  theorem 
Resolve_optimal: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ml : MeasureSet} {D : List Doc} {d_choiceless : Doc} {m : Meas},
  Resolve F d c i ml →
    Widen d D →
      d_choiceless ∈ D →
        MeasRender F d_choiceless c i m →
          m.y ≤ F.W →
            m.x ≤ F.W → ∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
Resolve_optimal 
      (
h_print: Resolve F d c i ml
h_print : 
Resolve: {α : Type} → Factory α → Doc → ℕ → ℕ → MeasureSet → Prop
Resolve 
F: ?m.4
F 
d: ?m.11
d 
c: ?m.17
c 
i: ?m.23
i 
ml: ?m.29
ml)
      (
h_widen: Widen d D
h_widen : 
Widen: Doc → List Doc → Prop
Widen 
d: ?m.11
d 
D: ?m.38
D) (
h_mem: d_choiceless ∈ D
h_mem : 
d_choiceless: ?m.63
d_choiceless ∈ 
D: ?m.38
D) 
      (
h_render: MeasRender F d_choiceless c i m
h_render : 
MeasRender: {α : Type} → Factory α → Doc → ℕ → ℕ → Meas → Prop
MeasRender 
F: ?m.4
F 
d_choiceless: ?m.63
d_choiceless 
c: ?m.17
c 
i: ?m.23
i 
m: ?m.102
m)
      (
h_y: m.y ≤ F.W
h_y : 
m: ?m.102
m.
y: {α : Type} → Meas → ℕ
y ≤ 
F: ?m.4
F.
W: {α : Type} → Factory α → ℕ
W) (
h_x: m.x ≤ F.W
h_x : 
m: ?m.102
m.
x: {α : Type} → Meas → ℕ
x ≤ 
F: ?m.4
F.
W: {α : Type} → Factory α → ℕ
W) :
      ∃ 
ms: ?m.164
ms 
h: ?m.169
h, 
ml: ?m.29
ml = 
MeasureSet.set: {α : Type} → (ms : List Meas) → ms ≠ [] → MeasureSet
MeasureSet.set 
ms: ?m.164
ms 
h: ?m.169
h ∧ ∃ 
m_better: ?m.204
m_better, 
m_better: ?m.204
m_better ∈ 
ms: ?m.164
ms ∧ 
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates 
F: ?m.4
F 
m_better: ?m.204
m_better 
m: ?m.102
m := by
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_print: Resolve F d c i ml

h_widen: Widen d D

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truematch 
d: Doc
d with
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_print: Resolve F d c i ml

h_widen: Widen d D

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true| 
Doc.text: String → Doc
Doc.text 
s: String
s =>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_print: Resolve F d c i ml

h_widen: Widen d D

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueapply 
Resolve_optimal_text: ∀ {α : Type} {F : Factory α} {s : String} {c i : ℕ} {ml : MeasureSet} {D : List Doc} {d_choiceless : Doc} {m : Meas},
  Resolve F (Doc.text s) c i ml →
    Widen (Doc.text s) D →
      d_choiceless ∈ D →
        MeasRender F d_choiceless c i m →
          m.y ≤ F.W →
            m.x ≤ F.W → ∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
Resolve_optimal_text
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

h_print
Resolve F (Doc.text ?s) ?c ?i ml
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

h_widen
Widen (Doc.text ?s) ?D
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

h_mem
?d_choiceless ∈ ?D
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

h_render
MeasRender F ?d_choiceless ?c ?i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

h_y
m.y ≤ F.W
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

h_x
m.x ≤ F.W
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

s
String
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

c
ℕ
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

i
ℕ
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

D
List Doc
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

d_choiceless
Doc 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true<;>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

h_print
Resolve F (Doc.text ?s) ?c ?i ml
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

h_widen
Widen (Doc.text ?s) ?D
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

h_mem
?d_choiceless ∈ ?D
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

h_render
MeasRender F ?d_choiceless ?c ?i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

h_y
m.y ≤ F.W
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

h_x
m.x ≤ F.W
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

s
String
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

c
ℕ
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

i
ℕ
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

D
List Doc
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

d_choiceless
Doc 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

s: String

h_print: Resolve F (Doc.text s) c i ml

h_widen: Widen (Doc.text s) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueassumption
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_print: Resolve F d c i ml

h_widen: Widen d D

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true| 
Doc.nl: Doc
Doc.nl =>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_print: Resolve F d c i ml

h_widen: Widen d D

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueapply 
Resolve_optimal_nl: ∀ {α : Type} {F : Factory α} {c i : ℕ} {ml : MeasureSet} {D : List Doc} {d_choiceless : Doc} {m : Meas},
  Resolve F Doc.nl c i ml →
    Widen Doc.nl D →
      d_choiceless ∈ D →
        MeasRender F d_choiceless c i m →
          m.y ≤ F.W →
            m.x ≤ F.W → ∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
Resolve_optimal_nl
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

h_print
Resolve F Doc.nl ?c ?i ml
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

h_widen
Widen Doc.nl ?D
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

h_mem
?d_choiceless ∈ ?D
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

h_render
MeasRender F ?d_choiceless ?c ?i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

h_y
m.y ≤ F.W
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

h_x
m.x ≤ F.W
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

c
ℕ
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

i
ℕ
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

D
List Doc
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

d_choiceless
Doc 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true<;>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

h_print
Resolve F Doc.nl ?c ?i ml
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

h_widen
Widen Doc.nl ?D
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

h_mem
?d_choiceless ∈ ?D
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

h_render
MeasRender F ?d_choiceless ?c ?i m
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

h_y
m.y ≤ F.W
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

h_x
m.x ≤ F.W
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

c
ℕ
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

i
ℕ
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

D
List Doc
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

d_choiceless
Doc 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

h_print: Resolve F Doc.nl c i ml

h_widen: Widen Doc.nl D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueassumption
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_print: Resolve F d c i ml

h_widen: Widen d D

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true| 
Doc.nest: ℕ → Doc → Doc
Doc.nest 
n: ℕ
n 
d: Doc
d =>
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

h_print: Resolve F (Doc.nest n d) c i ml

h_widen: Widen (Doc.nest n d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_print: Resolve F d c i ml

h_widen: Widen d D

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_widen: Widen (Doc.nest n d) D
h_widen
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

h_print: Resolve F (Doc.nest n d) c i ml

L✝: List Doc

h✝: Widen d L✝

h_mem: d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝

nest
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
      
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

h_print: Resolve F (Doc.nest n d) c i ml

h_widen: Widen (Doc.nest n d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truerename_i 
h_widen: Widen d L✝
h_widen
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

h_print: Resolve F (Doc.nest n d) c i ml

L✝: List Doc

h_widen: Widen d L✝

h_mem: d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝

nest
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

h_print: Resolve F (Doc.nest n d) c i ml

h_widen: Widen (Doc.nest n d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp at 
h_mem: d_choiceless ∈ List.map (fun d => Doc.nest n d) L✝
h_mem
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

h_print: Resolve F (Doc.nest n d) c i ml

L✝: List Doc

h_widen: Widen d L✝

h_mem: ∃ a, a ∈ L✝ ∧ Doc.nest n a = d_choiceless

nest
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

h_print: Resolve F (Doc.nest n d) c i ml

h_widen: Widen (Doc.nest n d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truelet ⟨
_: Doc
_, ⟨
h_left: w✝ ∈ L✝
h_left, 
h_right: Doc.nest n w✝ = d_choiceless
h_right⟩⟩ := 
h_mem: ∃ a, a ∈ L✝ ∧ Doc.nest n a = d_choiceless
h_mem
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

h_print: Resolve F (Doc.nest n d) c i ml

L✝: List Doc

h_widen: Widen d L✝

h_mem: ∃ a, a ∈ L✝ ∧ Doc.nest n a = d_choiceless

w✝: Doc

h_left: w✝ ∈ L✝

h_right: Doc.nest n w✝ = d_choiceless

nest
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

h_print: Resolve F (Doc.nest n d) c i ml

h_widen: Widen (Doc.nest n d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesubst 
h_right: Doc.nest n w✝ = d_choiceless
h_right
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

h_print: Resolve F (Doc.nest n d) c i ml

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.nest n a = Doc.nest n w✝

nest
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

h_print: Resolve F (Doc.nest n d) c i ml

h_widen: Widen (Doc.nest n d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

h_print: Resolve F (Doc.nest n d) c i ml

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.nest n a = Doc.nest n w✝

nest
∃ ms, (∃ x, ml = MeasureSet.set ms x) ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

h_print: Resolve F (Doc.nest n d) c i ml

h_widen: Widen (Doc.nest n d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_print: Resolve F (Doc.nest n d) c i ml
h_print
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.nest n a = Doc.nest n w✝

ms✝: MeasureSet

h✝: Resolve F d c (i + n) ms✝

nest.nest
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) ms✝ = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
      
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

h_print: Resolve F (Doc.nest n d) c i ml

h_widen: Widen (Doc.nest n d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase nest 
ms': MeasureSet
ms' 
h': Resolve F d c (i + n) ms'
h' => 
        
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.nest n a = Doc.nest n w✝

ms': MeasureSet

h': Resolve F d c (i + n) ms'

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) ms' = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp at *
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

ms': MeasureSet

h': Resolve F d c (i + n) ms'

h_mem: w✝ ∈ L✝

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) ms' = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
        
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.nest n a = Doc.nest n w✝

ms': MeasureSet

h': Resolve F d c (i + n) ms'

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) ms' = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
ms': MeasureSet
ms'
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c (i + n) (MeasureSet.tainted m✝)

tainted
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d c (i + n) (MeasureSet.set ms✝ h✝)

set
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
        
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.nest n a = Doc.nest n w✝

ms': MeasureSet

h': Resolve F d c (i + n) ms'

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) ms' = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase tainted => 
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c (i + n) (MeasureSet.tainted m✝)

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_render: MeasRender F (Doc.nest n w✝) c i m
h_render
α✝: Type

F: Factory α✝

d✝: Doc

c, i, n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left, h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c (i + n) (MeasureSet.tainted m✝)

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h✝: MeasRender F w✝ c (i + n) { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.x ≤ F.W

nest
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c (i + n) (MeasureSet.tainted m✝)

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truerename_i 
h_render: MeasRender F w✝ c (i + n) { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }
h_render
α✝: Type

F: Factory α✝

d✝: Doc

c, i, n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left, h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c (i + n) (MeasureSet.tainted m✝)

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c (i + n) { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.x ≤ F.W

nest
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c (i + n) (MeasureSet.tainted m✝)

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp
α✝: Type

F: Factory α✝

d✝: Doc

c, i, n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left, h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c (i + n) (MeasureSet.tainted m✝)

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c (i + n) { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.x ≤ F.W

nest
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ } = true 
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c (i + n) (MeasureSet.tainted m✝)

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truehave := 
Resolve_optimal: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ml : MeasureSet} {D : List Doc} {d_choiceless : Doc} {m : Meas},
  Resolve F d c i ml →
    Widen d D →
      d_choiceless ∈ D →
        MeasRender F d_choiceless c i m →
          m.y ≤ F.W →
            m.x ≤ F.W → ∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
Resolve_optimal 
h': Resolve F d c (i + n) (MeasureSet.tainted m✝)
h' 
h_widen: Widen d L✝
h_widen 
h_left: w✝ ∈ L✝
h_left (
α✝: Type

F: Factory α✝

d✝: Doc

c, i, n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left, h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c (i + n) (MeasureSet.tainted m✝)

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c (i + n) { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.x ≤ F.W

nest
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ } = trueby
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

d✝: Doc

c, i, n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left, h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c (i + n) (MeasureSet.tainted m✝)

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c (i + n) { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.x ≤ F.W

MeasRender F w✝ c (i + n) ?m.14220assumption
Goals accomplished! 🐙)
α✝: Type

F: Factory α✝

d✝: Doc

c, i, n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left, h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c (i + n) (MeasureSet.tainted m✝)

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c (i + n) { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.x ≤ F.W

this: { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }.y ≤ F.W →
  { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }.x ≤ F.W →
    ∃ ms h,
      MeasureSet.tainted m✝ = MeasureSet.set ms h ∧         ∃ m_better,
          m_better ∈ ms ∧ dominates F m_better { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ } = true

nest
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c (i + n) (MeasureSet.tainted m✝)

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp at 
this: ?m.14211
this 
h_x: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.x ≤ F.W
h_x 
h_y: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.y ≤ F.W
h_y
α✝: Type

F: Factory α✝

d✝: Doc

c, i, n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left, h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c (i + n) (MeasureSet.tainted m✝)

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c (i + n) { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: y✝ ≤ F.W

h_x: x✝ ≤ F.W

this: y✝ ≤ F.W → x✝ ≤ F.W → False

nest
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c (i + n) (MeasureSet.tainted m✝)

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
this: y✝ ≤ F.W → x✝ ≤ F.W → False
this 
h_y: y✝ ≤ F.W
h_y 
h_x: x✝ ≤ F.W
h_x
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.nest n a = Doc.nest n w✝

ms': MeasureSet

h': Resolve F d c (i + n) ms'

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) ms' = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase set 
printed_ms: List Meas
printed_ms 
h_render': printed_ms ≠ []
h_render' => 
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c (i + n) (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp [
MeasureSet.lift: {α : Type} → (Meas → Meas) → MeasureSet → MeasureSet
MeasureSet.lift, 
Meas.adjust_nest: {α : Type} → ℕ → Meas → Meas
Meas.adjust_nest]
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c (i + n) (MeasureSet.set printed_ms h_render')

∃ ms,
  (¬ms = [] ∧       List.map (fun x => { last := x.last, cost := x.cost, doc := Doc.nest n x.doc, x := x.x, y := x.y }) printed_ms =         ms) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c (i + n) (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_render: MeasRender F (Doc.nest n w✝) c i m
h_render
α✝: Type

F: Factory α✝

d✝: Doc

c, i, n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left, h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c (i + n) (MeasureSet.set printed_ms h_render')

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h✝: MeasRender F w✝ c (i + n) { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.x ≤ F.W

nest
∃ ms,
  (¬ms = [] ∧       List.map (fun x => { last := x.last, cost := x.cost, doc := Doc.nest n x.doc, x := x.x, y := x.y }) printed_ms =         ms) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c (i + n) (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truerename_i 
h_render: MeasRender F w✝ c (i + n) { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }
h_render
α✝: Type

F: Factory α✝

d✝: Doc

c, i, n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left, h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c (i + n) (MeasureSet.set printed_ms h_render')

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c (i + n) { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.x ≤ F.W

nest
∃ ms,
  (¬ms = [] ∧       List.map (fun x => { last := x.last, cost := x.cost, doc := Doc.nest n x.doc, x := x.x, y := x.y }) printed_ms =         ms) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c (i + n) (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truehave 
h_now: ?m.21780
h_now := 
Resolve_optimal: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ml : MeasureSet} {D : List Doc} {d_choiceless : Doc} {m : Meas},
  Resolve F d c i ml →
    Widen d D →
      d_choiceless ∈ D →
        MeasRender F d_choiceless c i m →
          m.y ≤ F.W →
            m.x ≤ F.W → ∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
Resolve_optimal 
h': Resolve F d c (i + n) (MeasureSet.set printed_ms h_render')
h' 
h_widen: Widen d L✝
h_widen 
h_left: w✝ ∈ L✝
h_left 
h_render: MeasRender F w✝ c (i + n) { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }
h_render 
h_y: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.y ≤ F.W
h_y 
h_x: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.x ≤ F.W
h_x
α✝: Type

F: Factory α✝

d✝: Doc

c, i, n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left, h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c (i + n) (MeasureSet.set printed_ms h_render')

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c (i + n) { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.x ≤ F.W

h_now: ∃ ms h,
  MeasureSet.set printed_ms h_render' = MeasureSet.set ms h ∧     ∃ m_better,
      m_better ∈ ms ∧ dominates F m_better { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ } = true

nest
∃ ms,
  (¬ms = [] ∧       List.map (fun x => { last := x.last, cost := x.cost, doc := Doc.nest n x.doc, x := x.x, y := x.y }) printed_ms =         ms) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c (i + n) (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp [
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates] at 
h_now: ?m.21780
h_now
α✝: Type

F: Factory α✝

d✝: Doc

c, i, n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left, h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c (i + n) (MeasureSet.set printed_ms h_render')

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c (i + n) { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.x ≤ F.W

h_now: ¬printed_ms = [] ∧ ∃ m_better, m_better ∈ printed_ms ∧ m_better.last ≤ last✝ ∧ Factory.le F m_better.cost cost✝ = true

nest
∃ ms,
  (¬ms = [] ∧       List.map (fun x => { last := x.last, cost := x.cost, doc := Doc.nest n x.doc, x := x.x, y := x.y }) printed_ms =         ms) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c (i + n) (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueexists 
printed_ms: List Meas
printed_ms.
map: {α : Type ?u.26642} → {β : Type ?u.26641} → (α → β) → List α → List β
map (
Meas.adjust_nest: {α : Type} → ℕ → Meas → Meas
Meas.adjust_nest 
n: ℕ
n)
α✝: Type

F: Factory α✝

d✝: Doc

c, i, n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left, h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c (i + n) (MeasureSet.set printed_ms h_render')

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c (i + n) { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.x ≤ F.W

h_now: ¬printed_ms = [] ∧ ∃ m_better, m_better ∈ printed_ms ∧ m_better.last ≤ last✝ ∧ Factory.le F m_better.cost cost✝ = true

nest
(¬List.map (Meas.adjust_nest n) printed_ms = [] ∧     List.map (fun x => { last := x.last, cost := x.cost, doc := Doc.nest n x.doc, x := x.x, y := x.y }) printed_ms =       List.map (Meas.adjust_nest n) printed_ms) ∧   ∃ m_better,
    m_better ∈ List.map (Meas.adjust_nest n) printed_ms ∧       dominates F m_better { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c (i + n) (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp [
Meas.adjust_nest: {α : Type} → ℕ → Meas → Meas
Meas.adjust_nest, 
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates]
α✝: Type

F: Factory α✝

d✝: Doc

c, i, n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left, h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c (i + n) (MeasureSet.set printed_ms h_render')

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c (i + n) { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.nest n w✝, x := x✝, y := y✝ }.x ≤ F.W

h_now: ¬printed_ms = [] ∧ ∃ m_better, m_better ∈ printed_ms ∧ m_better.last ≤ last✝ ∧ Factory.le F m_better.cost cost✝ = true

nest
¬printed_ms = [] ∧ ∃ a, a ∈ printed_ms ∧ a.last ≤ last✝ ∧ Factory.le F a.cost cost✝ = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

n: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.nest n w✝) c i m

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c (i + n) (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_nest n) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueassumption
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_print: Resolve F d c i ml

h_widen: Widen d D

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true| 
Doc.align: Doc → Doc
Doc.align 
d: Doc
d =>
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

h_print: Resolve F (Doc.align d) c i ml

h_widen: Widen (Doc.align d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_print: Resolve F d c i ml

h_widen: Widen d D

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_widen: Widen (Doc.align d) D
h_widen
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

h_print: Resolve F (Doc.align d) c i ml

L✝: List Doc

h✝: Widen d L✝

h_mem: d_choiceless ∈ List.map (fun d => Doc.align d) L✝

align
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
      
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

h_print: Resolve F (Doc.align d) c i ml

h_widen: Widen (Doc.align d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truerename_i 
h_widen: Widen d L✝
h_widen
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

h_print: Resolve F (Doc.align d) c i ml

L✝: List Doc

h_widen: Widen d L✝

h_mem: d_choiceless ∈ List.map (fun d => Doc.align d) L✝

align
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

h_print: Resolve F (Doc.align d) c i ml

h_widen: Widen (Doc.align d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp at 
h_mem: d_choiceless ∈ List.map (fun d => Doc.align d) L✝
h_mem
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

h_print: Resolve F (Doc.align d) c i ml

L✝: List Doc

h_widen: Widen d L✝

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = d_choiceless

align
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

h_print: Resolve F (Doc.align d) c i ml

h_widen: Widen (Doc.align d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truelet ⟨
_: Doc
_, ⟨
h_left: w✝ ∈ L✝
h_left, 
h_right: Doc.align w✝ = d_choiceless
h_right⟩⟩ := 
h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = d_choiceless
h_mem
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

h_print: Resolve F (Doc.align d) c i ml

L✝: List Doc

h_widen: Widen d L✝

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = d_choiceless

w✝: Doc

h_left: w✝ ∈ L✝

h_right: Doc.align w✝ = d_choiceless

align
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

h_print: Resolve F (Doc.align d) c i ml

h_widen: Widen (Doc.align d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesubst 
h_right: Doc.align w✝ = d_choiceless
h_right
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

h_print: Resolve F (Doc.align d) c i ml

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = Doc.align w✝

align
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

h_print: Resolve F (Doc.align d) c i ml

h_widen: Widen (Doc.align d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

h_print: Resolve F (Doc.align d) c i ml

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = Doc.align w✝

align
∃ ms, (∃ x, ml = MeasureSet.set ms x) ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

h_print: Resolve F (Doc.align d) c i ml

h_widen: Widen (Doc.align d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_print: Resolve F (Doc.align d) c i ml
h_print
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = Doc.align w✝

ms✝: MeasureSet

h✝: Resolve F d c c ms✝

h_bad✝: i > F.W

align.align_taint
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = Doc.align w✝

ms✝: MeasureSet

h✝: Resolve F d c c ms✝

h_ok✝: i ≤ F.W

align.align
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) ms✝ = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
      
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

h_print: Resolve F (Doc.align d) c i ml

h_widen: Widen (Doc.align d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase align 
ms': MeasureSet
ms' 
h': Resolve F d c c ms'
h' _ => 
        
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = Doc.align w✝

ms': MeasureSet

h': Resolve F d c c ms'

h_ok✝: i ≤ F.W

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) ms' = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp at *
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

ms': MeasureSet

h': Resolve F d c c ms'

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) ms' = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
        
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = Doc.align w✝

ms': MeasureSet

h': Resolve F d c c ms'

h_ok✝: i ≤ F.W

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) ms' = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
ms': MeasureSet
ms'
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c c (MeasureSet.tainted m✝)

tainted
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

ms✝: List Meas

h✝: ms✝ ≠ []

h': Resolve F d c c (MeasureSet.set ms✝ h✝)

set
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
        
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = Doc.align w✝

ms': MeasureSet

h': Resolve F d c c ms'

h_ok✝: i ≤ F.W

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) ms' = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase tainted => 
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c c (MeasureSet.tainted m✝)

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_render: MeasRender F (Doc.align w✝) c i m
h_render
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c c (MeasureSet.tainted m✝)

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h✝: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.x ≤ F.W

align
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c c (MeasureSet.tainted m✝)

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truerename_i 
h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }
h_render
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c c (MeasureSet.tainted m✝)

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.x ≤ F.W

align
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c c (MeasureSet.tainted m✝)

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c c (MeasureSet.tainted m✝)

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.x ≤ F.W

align
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true 
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c c (MeasureSet.tainted m✝)

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truehave := 
Resolve_optimal: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ml : MeasureSet} {D : List Doc} {d_choiceless : Doc} {m : Meas},
  Resolve F d c i ml →
    Widen d D →
      d_choiceless ∈ D →
        MeasRender F d_choiceless c i m →
          m.y ≤ F.W →
            m.x ≤ F.W → ∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
Resolve_optimal 
h': Resolve F d c c (MeasureSet.tainted m✝)
h' 
h_widen: Widen d L✝
h_widen 
h_left: w✝ ∈ L✝
h_left (
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c c (MeasureSet.tainted m✝)

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.x ≤ F.W

align
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = trueby
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c c (MeasureSet.tainted m✝)

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.x ≤ F.W

MeasRender F w✝ c c ?m.53971assumption
Goals accomplished! 🐙)
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c c (MeasureSet.tainted m✝)

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.x ≤ F.W

this: { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }.y ≤ F.W →
  { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }.x ≤ F.W →
    ∃ ms h,
      MeasureSet.tainted m✝ = MeasureSet.set ms h ∧         ∃ m_better,
          m_better ∈ ms ∧ dominates F m_better { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ } = true

align
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c c (MeasureSet.tainted m✝)

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp at 
this: ?m.53962
this 
h_x: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.x ≤ F.W
h_x 
h_y: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.y ≤ F.W
h_y
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c c (MeasureSet.tainted m✝)

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

this: y✝ ≤ F.W → x✝ ≤ F.W → False

h_y: i ≤ F.W ∧ y✝ ≤ F.W

align
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c c (MeasureSet.tainted m✝)

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truelet ⟨_, 
h_y: y✝ ≤ F.W
h_y⟩ := 
h_y: i ≤ F.W ∧ y✝ ≤ F.W
h_y
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c c (MeasureSet.tainted m✝)

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

this: y✝ ≤ F.W → x✝ ≤ F.W → False

h_y✝: i ≤ F.W ∧ y✝ ≤ F.W

left✝: i ≤ F.W

h_y: y✝ ≤ F.W

align
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

m✝: Meas

h': Resolve F d c c (MeasureSet.tainted m✝)

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.tainted m✝) = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
this: y✝ ≤ F.W → x✝ ≤ F.W → False
this 
h_y: y✝ ≤ F.W
h_y 
h_x: x✝ ≤ F.W
h_x
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = Doc.align w✝

ms': MeasureSet

h': Resolve F d c c ms'

h_ok✝: i ≤ F.W

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) ms' = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase set 
printed_ms: List Meas
printed_ms 
h_render': printed_ms ≠ []
h_render' => 
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp [
MeasureSet.lift: {α : Type} → (Meas → Meas) → MeasureSet → MeasureSet
MeasureSet.lift, 
Meas.adjust_nest: {α : Type} → ℕ → Meas → Meas
Meas.adjust_nest]
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

∃ ms,
  (¬ms = [] ∧ List.map (Meas.adjust_align i) printed_ms = ms) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_render: MeasRender F (Doc.align w✝) c i m
h_render
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h✝: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.x ≤ F.W

align
∃ ms,
  (¬ms = [] ∧ List.map (Meas.adjust_align i) printed_ms = ms) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truerename_i 
h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }
h_render
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.x ≤ F.W

align
∃ ms,
  (¬ms = [] ∧ List.map (Meas.adjust_align i) printed_ms = ms) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truehave 
h_now: ?m.62090
h_now := 
Resolve_optimal: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ml : MeasureSet} {D : List Doc} {d_choiceless : Doc} {m : Meas},
  Resolve F d c i ml →
    Widen d D →
      d_choiceless ∈ D →
        MeasRender F d_choiceless c i m →
          m.y ≤ F.W →
            m.x ≤ F.W → ∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
Resolve_optimal 
h': Resolve F d c c (MeasureSet.set printed_ms h_render')
h' 
h_widen: Widen d L✝
h_widen 
h_left: w✝ ∈ L✝
h_left 
h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }
h_render
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.x ≤ F.W

h_now: { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }.y ≤ F.W →
  { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }.x ≤ F.W →
    ∃ ms h,
      MeasureSet.set printed_ms h_render' = MeasureSet.set ms h ∧         ∃ m_better,
          m_better ∈ ms ∧ dominates F m_better { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ } = true

align
∃ ms,
  (¬ms = [] ∧ List.map (Meas.adjust_align i) printed_ms = ms) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp [
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates] at 
h_now: ?m.62090
h_now 
h_x: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.x ≤ F.W
h_x 
h_y: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.y ≤ F.W
h_y
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_now: y✝ ≤ F.W →
  x✝ ≤ F.W →
    ¬printed_ms = [] ∧       ∃ m_better, m_better ∈ printed_ms ∧ m_better.last ≤ last✝ ∧ Factory.le F m_better.cost cost✝ = true

h_y: i ≤ F.W ∧ y✝ ≤ F.W

align
∃ ms,
  (¬ms = [] ∧ List.map (Meas.adjust_align i) printed_ms = ms) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truelet ⟨_, 
h_y: y✝ ≤ F.W
h_y⟩ := 
h_y: i ≤ F.W ∧ y✝ ≤ F.W
h_y
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_now: y✝ ≤ F.W →
  x✝ ≤ F.W →
    ¬printed_ms = [] ∧       ∃ m_better, m_better ∈ printed_ms ∧ m_better.last ≤ last✝ ∧ Factory.le F m_better.cost cost✝ = true

h_y✝: i ≤ F.W ∧ y✝ ≤ F.W

left✝: i ≤ F.W

h_y: y✝ ≤ F.W

align
∃ ms,
  (¬ms = [] ∧ List.map (Meas.adjust_align i) printed_ms = ms) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truespecialize 
h_now: y✝ ≤ F.W →
  x✝ ≤ F.W →
    ¬printed_ms = [] ∧       ∃ m_better, m_better ∈ printed_ms ∧ m_better.last ≤ last✝ ∧ Factory.le F m_better.cost cost✝ = true
h_now 
h_y: y✝ ≤ F.W
h_y 
h_x: x✝ ≤ F.W
h_x
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y✝: i ≤ F.W ∧ y✝ ≤ F.W

left✝: i ≤ F.W

h_y: y✝ ≤ F.W

h_now: ¬printed_ms = [] ∧ ∃ m_better, m_better ∈ printed_ms ∧ m_better.last ≤ last✝ ∧ Factory.le F m_better.cost cost✝ = true

align
∃ ms,
  (¬ms = [] ∧ List.map (Meas.adjust_align i) printed_ms = ms) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueexists 
printed_ms: List Meas
printed_ms.
map: {α : Type ?u.70117} → {β : Type ?u.70116} → (α → β) → List α → List β
map (
Meas.adjust_align: {α : Type} → ℕ → Meas → Meas
Meas.adjust_align 
i: ℕ
i)
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y✝: i ≤ F.W ∧ y✝ ≤ F.W

left✝: i ≤ F.W

h_y: y✝ ≤ F.W

h_now: ¬printed_ms = [] ∧ ∃ m_better, m_better ∈ printed_ms ∧ m_better.last ≤ last✝ ∧ Factory.le F m_better.cost cost✝ = true

align
(¬List.map (Meas.adjust_align i) printed_ms = [] ∧     List.map (Meas.adjust_align i) printed_ms = List.map (Meas.adjust_align i) printed_ms) ∧   ∃ m_better,
    m_better ∈ List.map (Meas.adjust_align i) printed_ms ∧       dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp [
Meas.adjust_align: {α : Type} → ℕ → Meas → Meas
Meas.adjust_align, 
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates]
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_x: x✝ ≤ F.W

h_y✝: i ≤ F.W ∧ y✝ ≤ F.W

left✝: i ≤ F.W

h_y: y✝ ≤ F.W

h_now: ¬printed_ms = [] ∧ ∃ m_better, m_better ∈ printed_ms ∧ m_better.last ≤ last✝ ∧ Factory.le F m_better.cost cost✝ = true

align
¬printed_ms = [] ∧ ∃ a, a ∈ printed_ms ∧ a.last ≤ last✝ ∧ Factory.le F a.cost cost✝ = true
          
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_ok✝: i ≤ F.W

h_mem: w✝ ∈ L✝

printed_ms: List Meas

h_render': printed_ms ≠ []

h': Resolve F d c c (MeasureSet.set printed_ms h_render')

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.set printed_ms h_render') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueassumption
Goals accomplished! 🐙
      
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

h_print: Resolve F (Doc.align d) c i ml

h_widen: Widen (Doc.align d) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase align_taint 
ms': MeasureSet
ms' 
h: Resolve F d c c ms'
h 
h_bad: i > F.W
h_bad => 
        
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = Doc.align w✝

ms': MeasureSet

h: Resolve F d c c ms'

h_bad: i > F.W

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_render: MeasRender F (Doc.align w✝) c i m
h_render
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = Doc.align w✝

ms': MeasureSet

h: Resolve F d c c ms'

h_bad: i > F.W

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h✝: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.x ≤ F.W

align
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms') = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true
        
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = Doc.align w✝

ms': MeasureSet

h: Resolve F d c c ms'

h_bad: i > F.W

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truerename_i 
h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }
h_render
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = Doc.align w✝

ms': MeasureSet

h: Resolve F d c c ms'

h_bad: i > F.W

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_y: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.y ≤ F.W

h_x: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.x ≤ F.W

align
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms') = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true
        
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = Doc.align w✝

ms': MeasureSet

h: Resolve F d c c ms'

h_bad: i > F.W

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp at 
h_y: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.y ≤ F.W
h_y
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = Doc.align w✝

ms': MeasureSet

h: Resolve F d c c ms'

h_bad: i > F.W

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_render: MeasRender F w✝ c c { last := last✝, cost := cost✝, doc := w✝, x := x✝, y := y✝ }

h_x: { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ }.x ≤ F.W

h_y: i ≤ F.W ∧ y✝ ≤ F.W

align
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms') = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true 
        
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = Doc.align w✝

ms': MeasureSet

h: Resolve F d c c ms'

h_bad: i > F.W

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueclear * - 
h_y: i ≤ F.W ∧ y✝ ≤ F.W
h_y 
h_bad: i > F.W
h_bad
α✝: Type

F: Factory α✝

i: ℕ

w✝: Doc

ms': MeasureSet

h_bad: i > F.W

last✝: ℕ

cost✝: α✝

x✝, y✝: ℕ

h_y: i ≤ F.W ∧ y✝ ≤ F.W

align
∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms') = MeasureSet.set ms x) ∧     ∃ m_better,
      m_better ∈ ms ∧         dominates F m_better { last := last✝, cost := cost✝, doc := Doc.align w✝, x := x✝, y := max i y✝ } = true 
        
α✝: Type

F: Factory α✝

d✝: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d: Doc

L✝: List Doc

h_widen: Widen d L✝

w✝: Doc

h_left: w✝ ∈ L✝

h_render: MeasRender F (Doc.align w✝) c i m

h_mem: ∃ a, a ∈ L✝ ∧ Doc.align a = Doc.align w✝

ms': MeasureSet

h: Resolve F d c c ms'

h_bad: i > F.W

∃ ms,
  (∃ x, MeasureSet.lift (Meas.adjust_align i) (MeasureSet.taint ms') = MeasureSet.set ms x) ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truelinarith
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_print: Resolve F d c i ml

h_widen: Widen d D

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true| 
Doc.choice: Doc → Doc → Doc
Doc.choice 
d₁: Doc
d₁ 
d₂: Doc
d₂ =>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.choice d₁ d₂) c i ml

h_widen: Widen (Doc.choice d₁ d₂) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_print: Resolve F d c i ml

h_widen: Widen d D

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_widen: Widen (Doc.choice d₁ d₂) D
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.choice d₁ d₂) c i ml

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

h_mem: d_choiceless ∈ L₁✝ ++ L₂✝

choice
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.choice d₁ d₂) c i ml

h_widen: Widen (Doc.choice d₁ d₂) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truerename_i 
h_widen₁: Widen d₁ L₁✝
h_widen₁ 
h_widen₂: Widen d₂ L₂✝
h_widen₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.choice d₁ d₂) c i ml

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: d_choiceless ∈ L₁✝ ++ L₂✝

choice
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.choice d₁ d₂) c i ml

h_widen: Widen (Doc.choice d₁ d₂) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp at 
h_mem: d_choiceless ∈ L₁✝ ++ L₂✝
h_mem
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.choice d₁ d₂) c i ml

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: d_choiceless ∈ L₁✝ ∨ d_choiceless ∈ L₂✝

choice
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.choice d₁ d₂) c i ml

h_widen: Widen (Doc.choice d₁ d₂) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_print: Resolve F (Doc.choice d₁ d₂) c i ml
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: d_choiceless ∈ L₁✝ ∨ d_choiceless ∈ L₂✝

ms✝, ms'✝: MeasureSet

h_left✝: Resolve F d₁ c i ms✝

h_right✝: Resolve F d₂ c i ms'✝

choice.choice
∃ ms h, MeasureSet.union F ms✝ ms'✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.choice d₁ d₂) c i ml

h_widen: Widen (Doc.choice d₁ d₂) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase choice 
ms₁: MeasureSet
ms₁ 
ms₂: MeasureSet
ms₂ 
h_left: Resolve F d₁ c i ms₁
h_left 
h_right: Resolve F d₂ c i ms₂
h_right => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: d_choiceless ∈ L₁✝ ∨ d_choiceless ∈ L₂✝

ms₁, ms₂: MeasureSet

h_left: Resolve F d₁ c i ms₁

h_right: Resolve F d₂ c i ms₂

∃ ms h, MeasureSet.union F ms₁ ms₂ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
ms₁: MeasureSet
ms₁
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: d_choiceless ∈ L₁✝ ∨ d_choiceless ∈ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

tainted
∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: d_choiceless ∈ L₁✝ ∨ d_choiceless ∈ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

set
∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: d_choiceless ∈ L₁✝ ∨ d_choiceless ∈ L₂✝

ms₁, ms₂: MeasureSet

h_left: Resolve F d₁ c i ms₁

h_right: Resolve F d₂ c i ms₂

∃ ms h, MeasureSet.union F ms₁ ms₂ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase tainted => 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: d_choiceless ∈ L₁✝ ∨ d_choiceless ∈ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_mem: d_choiceless ∈ L₁✝ ∨ d_choiceless ∈ L₂✝
h_mem
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h✝: d_choiceless ∈ L₁✝

inl
∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h✝: d_choiceless ∈ L₂✝

inr
∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: d_choiceless ∈ L₁✝ ∨ d_choiceless ∈ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase inl 
h_mem: ?m.94326
h_mem => 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₁✝

∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truehave := 
Resolve_optimal: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ml : MeasureSet} {D : List Doc} {d_choiceless : Doc} {m : Meas},
  Resolve F d c i ml →
    Widen d D →
      d_choiceless ∈ D →
        MeasRender F d_choiceless c i m →
          m.y ≤ F.W →
            m.x ≤ F.W → ∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
Resolve_optimal 
h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)
h_left 
h_widen₁: Widen d₁ L₁✝
h_widen₁ 
h_mem: ?m.94326
h_mem (
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₁✝

∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueby
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₁✝

MeasRender F d_choiceless c i ?m.94380assumption
Goals accomplished! 🐙)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.tainted m✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₁✝

∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truelet ⟨
_: List Meas
_, 
_: w✝¹ ≠ []
_, _, _⟩ := 
this: ?m.94371
this 
h_y: m.y ≤ F.W
h_y 
h_x: m.x ≤ F.W
h_x
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.tainted m✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

w✝¹: List Meas

w✝: w✝¹ ≠ []

left✝: MeasureSet.tainted m✝ = MeasureSet.set w✝¹ w✝

right✝: ∃ m_better, m_better ∈ w✝¹ ∧ dominates F m_better m = true

∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₁✝

∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecontradiction
Goals accomplished! 🐙
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: d_choiceless ∈ L₁✝ ∨ d_choiceless ∈ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase inr 
h_mem: ?m.94327
h_mem => 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₂✝

∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truehave := 
Resolve_optimal: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ml : MeasureSet} {D : List Doc} {d_choiceless : Doc} {m : Meas},
  Resolve F d c i ml →
    Widen d D →
      d_choiceless ∈ D →
        MeasRender F d_choiceless c i m →
          m.y ≤ F.W →
            m.x ≤ F.W → ∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
Resolve_optimal 
h_right: Resolve F d₂ c i ms₂
h_right 
h_widen₂: Widen d₂ L₂✝
h_widen₂ 
h_mem: ?m.94327
h_mem (
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₂✝

∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueby
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₂✝

MeasRender F d_choiceless c i ?m.98688assumption
Goals accomplished! 🐙)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₂✝

this: m.y ≤ F.W → m.x ≤ F.W → ∃ ms h, ms₂ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₂✝

∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truelet ⟨
ms: List Meas
ms, 
_: ms ≠ []
_, 
h_left: ms₂ = MeasureSet.set ms w✝
h_left, 
h_right: ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
h_right⟩ := 
this: ?m.98679
this 
h_y: m.y ≤ F.W
h_y 
h_x: m.x ≤ F.W
h_x
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right✝: Resolve F d₂ c i ms₂

m✝: Meas

h_left✝: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₂✝

this: m.y ≤ F.W → m.x ≤ F.W → ∃ ms h, ms₂ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms: List Meas

w✝: ms ≠ []

h_left: ms₂ = MeasureSet.set ms w✝

h_right: ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₂✝

∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesubst 
h_left: ms₂ = MeasureSet.set ms w✝
h_left
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₂✝

ms: List Meas

w✝: ms ≠ []

h_right✝: ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_right: Resolve F d₂ c i (MeasureSet.set ms w✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms_1 h, MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧ ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m = true

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms w✝) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m = true
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₂✝

∃ ms h,
  MeasureSet.union F (MeasureSet.tainted m✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueexists 
ms: List Meas
ms, (
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₂✝

ms: List Meas

w✝: ms ≠ []

h_right✝: ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_right: Resolve F d₂ c i (MeasureSet.set ms w✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms_1 h, MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧ ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m = true

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms w✝) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m = trueby
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

m✝: Meas

h_left: Resolve F d₁ c i (MeasureSet.tainted m✝)

h_mem: d_choiceless ∈ L₂✝

ms: List Meas

w✝: ms ≠ []

h_right✝: ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_right: Resolve F d₂ c i (MeasureSet.set ms w✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms_1 h, MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧ ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m = true

ms ≠ []assumption
Goals accomplished! 🐙)
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: d_choiceless ∈ L₁✝ ∨ d_choiceless ∈ L₂✝

ms₁, ms₂: MeasureSet

h_left: Resolve F d₁ c i ms₁

h_right: Resolve F d₂ c i ms₂

∃ ms h, MeasureSet.union F ms₁ ms₂ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase set => 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: d_choiceless ∈ L₁✝ ∨ d_choiceless ∈ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_mem: d_choiceless ∈ L₁✝ ∨ d_choiceless ∈ L₂✝
h_mem
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝¹: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝¹)

h✝: d_choiceless ∈ L₁✝

inl
∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝¹) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝¹: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝¹)

h✝: d_choiceless ∈ L₂✝

inr
∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝¹) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: d_choiceless ∈ L₁✝ ∨ d_choiceless ∈ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase inl 
h_mem: ?m.105539
h_mem => 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truehave := 
Resolve_optimal: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ml : MeasureSet} {D : List Doc} {d_choiceless : Doc} {m : Meas},
  Resolve F d c i ml →
    Widen d D →
      d_choiceless ∈ D →
        MeasRender F d_choiceless c i m →
          m.y ≤ F.W →
            m.x ≤ F.W → ∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
Resolve_optimal 
h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)
h_left 
h_widen₁: Widen d₁ L₁✝
h_widen₁ 
h_mem: ?m.105539
h_mem (
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueby
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

MeasRender F d_choiceless c i ?m.105593assumption
Goals accomplished! 🐙)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truelet ⟨
ms_left: List Meas
ms_left, 
_: ms_left ≠ []
_, 
h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set ms_left w✝
h_left', 
h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true
h_right'⟩ := 
this: ?m.105584
this 
h_y: m.y ≤ F.W
h_y 
h_x: m.x ≤ F.W
h_x
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
ms₂: MeasureSet
ms₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

m✝: Meas

h_right: Resolve F d₂ c i (MeasureSet.tainted m✝)

tainted
∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.tainted m✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

set
∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝¹ h✝¹) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase tainted => 
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

m✝: Meas

h_right: Resolve F d₂ c i (MeasureSet.tainted m✝)

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.tainted m✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp [
MeasureSet.union: {α : Type} → Factory α → MeasureSet → MeasureSet → MeasureSet
MeasureSet.union]
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

m✝: Meas

h_right: Resolve F d₂ c i (MeasureSet.tainted m✝)

¬ms✝ = [] ∧ ∃ m_better, m_better ∈ ms✝ ∧ dominates F m_better m = true
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

m✝: Meas

h_right: Resolve F d₂ c i (MeasureSet.tainted m✝)

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.tainted m✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp at 
h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set ms_left w✝
h_left'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

m✝: Meas

h_right: Resolve F d₂ c i (MeasureSet.tainted m✝)

h_left': ms✝ = ms_left

¬ms✝ = [] ∧ ∃ m_better, m_better ∈ ms✝ ∧ dominates F m_better m = true 
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

m✝: Meas

h_right: Resolve F d₂ c i (MeasureSet.tainted m✝)

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.tainted m✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesubst 
h_left': ms✝ = ms_left
h_left'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

m✝: Meas

h_right: Resolve F d₂ c i (MeasureSet.tainted m✝)

w✝: ms✝ ≠ []

h_right': ∃ m_better, m_better ∈ ms✝ ∧ dominates F m_better m = true

¬ms✝ = [] ∧ ∃ m_better, m_better ∈ ms✝ ∧ dominates F m_better m = true
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

m✝: Meas

h_right: Resolve F d₂ c i (MeasureSet.tainted m✝)

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.tainted m✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueconstructor
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

m✝: Meas

h_right: Resolve F d₂ c i (MeasureSet.tainted m✝)

w✝: ms✝ ≠ []

h_right': ∃ m_better, m_better ∈ ms✝ ∧ dominates F m_better m = true

left
¬ms✝ = []
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

m✝: Meas

h_right: Resolve F d₂ c i (MeasureSet.tainted m✝)

w✝: ms✝ ≠ []

h_right': ∃ m_better, m_better ∈ ms✝ ∧ dominates F m_better m = true

right
∃ m_better, m_better ∈ ms✝ ∧ dominates F m_better m = true 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

m✝: Meas

h_right: Resolve F d₂ c i (MeasureSet.tainted m✝)

w✝: ms✝ ≠ []

h_right': ∃ m_better, m_better ∈ ms✝ ∧ dominates F m_better m = true

¬ms✝ = [] ∧ ∃ m_better, m_better ∈ ms✝ ∧ dominates F m_better m = true<;>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

m✝: Meas

h_right: Resolve F d₂ c i (MeasureSet.tainted m✝)

w✝: ms✝ ≠ []

h_right': ∃ m_better, m_better ∈ ms✝ ∧ dominates F m_better m = true

left
¬ms✝ = []
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

m✝: Meas

h_right: Resolve F d₂ c i (MeasureSet.tainted m✝)

w✝: ms✝ ≠ []

h_right': ∃ m_better, m_better ∈ ms✝ ∧ dominates F m_better m = true

right
∃ m_better, m_better ∈ ms✝ ∧ dominates F m_better m = true 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

m✝: Meas

h_right: Resolve F d₂ c i (MeasureSet.tainted m✝)

w✝: ms✝ ≠ []

h_right': ∃ m_better, m_better ∈ ms✝ ∧ dominates F m_better m = true

¬ms✝ = [] ∧ ∃ m_better, m_better ∈ ms✝ ∧ dominates F m_better m = trueassumption
Goals accomplished! 🐙
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₁✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase set => 
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝¹ h✝¹) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truelet ⟨
m_better: Meas
m_better, 
h_mem_b: m_better ∈ ms_left
h_mem_b, _⟩ := 
h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true
h_right'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better: Meas

h_mem_b: m_better ∈ ms_left

right✝: dominates F m_better m = true

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝¹ h✝¹) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝¹ h✝¹) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp [
MeasureSet.union: {α : Type} → Factory α → MeasureSet → MeasureSet → MeasureSet
MeasureSet.union]
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better: Meas

h_mem_b: m_better ∈ ms_left

right✝: dominates F m_better m = true

¬merge F (ms✝¹, ms✝) = [] ∧ ∃ m_better, m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = true
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝¹ h✝¹) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueconstructor
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better: Meas

h_mem_b: m_better ∈ ms_left

right✝: dominates F m_better m = true

left
¬merge F (ms✝¹, ms✝) = []
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better: Meas

h_mem_b: m_better ∈ ms_left

right✝: dominates F m_better m = true

right
∃ m_better, m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = true 
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝¹ h✝¹) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase left => 
                
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better: Meas

h_mem_b: m_better ∈ ms_left

right✝: dominates F m_better m = true

¬merge F (ms✝¹, ms✝) = []apply 
merge_not_empty: ∀ {α : Type} {ms₁ ms₂ : List Meas} {F : Factory α}, ms₁ ≠ [] ∨ ms₂ ≠ [] → merge F (ms₁, ms₂) ≠ []
merge_not_empty
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better: Meas

h_mem_b: m_better ∈ ms_left

right✝: dominates F m_better m = true

h
ms✝¹ ≠ [] ∨ ms✝ ≠ []
                
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better: Meas

h_mem_b: m_better ∈ ms_left

right✝: dominates F m_better m = true

¬merge F (ms✝¹, ms✝) = []simp [*]
Goals accomplished! 🐙
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝¹ h✝¹) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase right => 
                
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better: Meas

h_mem_b: m_better ∈ ms_left

right✝: dominates F m_better m = true

∃ m_better, m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = truecases 
h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝
h_left'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better: Meas

right✝: dominates F m_better m = true

w✝: ms✝¹ ≠ []

h_right': ∃ m_better, m_better ∈ ms✝¹ ∧ dominates F m_better m = true

h_mem_b: m_better ∈ ms✝¹

refl
∃ m_better, m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = true
                
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better: Meas

h_mem_b: m_better ∈ ms_left

right✝: dominates F m_better m = true

∃ m_better, m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = truelet ⟨
m_better: Meas
m_better, ⟨
h_mem: m_better ∈ merge F (ms✝¹, ms✝)
h_mem, 
h_dom: dominates F m_better m_better✝ = true
h_dom⟩⟩ := 
merge_dom₁: ∀ {α : Type} {F : Factory α} {ms₁ ms₂ : List Meas} {m : Meas},
  pareto F ms₁ → pareto F ms₂ → m ∈ ms₁ → ∃ m_better, m_better ∈ merge F (ms₁, ms₂) ∧ dominates F m_better m = true
merge_dom₁ (
Resolve_pareto: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h_non_empty : ms ≠ []},
  Resolve F d c i (MeasureSet.set ms h_non_empty) → pareto F ms
Resolve_pareto 
h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)
h_left) (
Resolve_pareto: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h_non_empty : ms ≠ []},
  Resolve F d c i (MeasureSet.set ms h_non_empty) → pareto F ms
Resolve_pareto 
h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)
h_right) 
h_mem_b: m_better ∈ ms✝¹
h_mem_b
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem✝: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better✝: Meas

right✝: dominates F m_better✝ m = true

w✝: ms✝¹ ≠ []

h_right': ∃ m_better, m_better ∈ ms✝¹ ∧ dominates F m_better m = true

h_mem_b: m_better✝ ∈ ms✝¹

m_better: Meas

h_mem: m_better ∈ merge F (ms✝¹, ms✝)

h_dom: dominates F m_better m_better✝ = true

refl
∃ m_better, m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = true
                
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better: Meas

h_mem_b: m_better ∈ ms_left

right✝: dominates F m_better m = true

∃ m_better, m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = trueexists 
m_better: Meas
m_better
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem✝: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better✝: Meas

right✝: dominates F m_better✝ m = true

w✝: ms✝¹ ≠ []

h_right': ∃ m_better, m_better ∈ ms✝¹ ∧ dominates F m_better m = true

h_mem_b: m_better✝ ∈ ms✝¹

m_better: Meas

h_mem: m_better ∈ merge F (ms✝¹, ms✝)

h_dom: dominates F m_better m_better✝ = true

refl
m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = true 
                
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better: Meas

h_mem_b: m_better ∈ ms_left

right✝: dominates F m_better m = true

∃ m_better, m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = truesimp [*]
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem✝: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better✝: Meas

right✝: dominates F m_better✝ m = true

w✝: ms✝¹ ≠ []

h_right': ∃ m_better, m_better ∈ ms✝¹ ∧ dominates F m_better m = true

h_mem_b: m_better✝ ∈ ms✝¹

m_better: Meas

h_mem: m_better ∈ merge F (ms✝¹, ms✝)

h_dom: dominates F m_better m_better✝ = true

refl
dominates F m_better m = true
                
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms_left: List Meas

w✝: ms_left ≠ []

h_left': MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms_left w✝

h_right': ∃ m_better, m_better ∈ ms_left ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better: Meas

h_mem_b: m_better ∈ ms_left

right✝: dominates F m_better m = true

∃ m_better, m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = truedwi { 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem✝: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better✝: Meas

right✝: dominates F m_better✝ m = true

w✝: ms✝¹ ≠ []

h_right': ∃ m_better, m_better ∈ ms✝¹ ∧ dominates F m_better m = true

h_mem_b: m_better✝ ∈ ms✝¹

m_better: Meas

h_mem: m_better ∈ merge F (ms✝¹, ms✝)

h_dom: dominates F m_better m_better✝ = true

refl
dominates F m_better m = trueapply 
dominates_trans: ∀ {α : Type} {m₁ m₂ m₃ : Meas} {F : Factory α},
  dominates F m₁ m₂ = true → dominates F m₂ m₃ = true → dominates F m₁ m₃ = true
dominates_trans
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem✝: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better✝: Meas

right✝: dominates F m_better✝ m = true

w✝: ms✝¹ ≠ []

h_right': ∃ m_better, m_better ∈ ms✝¹ ∧ dominates F m_better m = true

h_mem_b: m_better✝ ∈ ms✝¹

m_better: Meas

h_mem: m_better ∈ merge F (ms✝¹, ms✝)

h_dom: dominates F m_better m_better✝ = true

refl.h
dominates F m_better ?refl.m₂ = true
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem✝: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better✝: Meas

right✝: dominates F m_better✝ m = true

w✝: ms✝¹ ≠ []

h_right': ∃ m_better, m_better ∈ ms✝¹ ∧ dominates F m_better m = true

h_mem_b: m_better✝ ∈ ms✝¹

m_better: Meas

h_mem: m_better ∈ merge F (ms✝¹, ms✝)

h_dom: dominates F m_better m_better✝ = true

refl.h'
dominates F ?refl.m₂ m = true
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem✝: d_choiceless ∈ L₁✝

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝¹ h✝¹ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

m_better✝: Meas

right✝: dominates F m_better✝ m = true

w✝: ms✝¹ ≠ []

h_right': ∃ m_better, m_better ∈ ms✝¹ ∧ dominates F m_better m = true

h_mem_b: m_better✝ ∈ ms✝¹

m_better: Meas

h_mem: m_better ∈ merge F (ms✝¹, ms✝)

h_dom: dominates F m_better m_better✝ = true

refl.m₂
Meas }
Goals accomplished! 🐙 
          
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: d_choiceless ∈ L₁✝ ∨ d_choiceless ∈ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase inr 
h_mem: ?m.105540
h_mem => 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₂✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truehave := 
Resolve_optimal: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ml : MeasureSet} {D : List Doc} {d_choiceless : Doc} {m : Meas},
  Resolve F d c i ml →
    Widen d D →
      d_choiceless ∈ D →
        MeasRender F d_choiceless c i m →
          m.y ≤ F.W →
            m.x ≤ F.W → ∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
Resolve_optimal 
h_right: Resolve F d₂ c i ms₂
h_right 
h_widen₂: Widen d₂ L₂✝
h_widen₂ 
h_mem: ?m.105540
h_mem (
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₂✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueby
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₂✝

MeasRender F d_choiceless c i ?m.131477assumption
Goals accomplished! 🐙)
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₂✝

this: m.y ≤ F.W → m.x ≤ F.W → ∃ ms h, ms₂ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₂✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truelet ⟨
_: List Meas
_, 
_: w✝¹ ≠ []
_, ⟨
h_left': ms₂ = MeasureSet.set w✝¹ w✝
h_left', 
m_better: Meas
m_better, 
h_mem_b: m_better ∈ w✝¹
h_mem_b, _⟩⟩ := 
this: ?m.131468
this 
h_y: m.y ≤ F.W
h_y 
h_x: m.x ≤ F.W
h_x
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₂✝

this: m.y ≤ F.W → m.x ≤ F.W → ∃ ms h, ms₂ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

w✝¹: List Meas

w✝: w✝¹ ≠ []

h_left': ms₂ = MeasureSet.set w✝¹ w✝

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₂✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
ms₂: MeasureSet
ms₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

m✝: Meas

h_right: Resolve F d₂ c i (MeasureSet.tainted m✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.tainted m✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.tainted m✝ = MeasureSet.set w✝¹ w✝

tainted
∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.tainted m✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝

set
∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝¹ h✝¹) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₂✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase tainted => 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

m✝: Meas

h_right: Resolve F d₂ c i (MeasureSet.tainted m✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.tainted m✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.tainted m✝ = MeasureSet.set w✝¹ w✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.tainted m✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp at 
h_left': MeasureSet.tainted m✝ = MeasureSet.set w✝¹ w✝
h_left'
Goals accomplished! 🐙 
            
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms₂: MeasureSet

h_right: Resolve F d₂ c i ms₂

ms✝: List Meas

h✝: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝)

h_mem: d_choiceless ∈ L₂✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) ms₂ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase set => 
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝¹ h✝¹) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp [
MeasureSet.union: {α : Type} → Factory α → MeasureSet → MeasureSet → MeasureSet
MeasureSet.union]
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝

¬merge F (ms✝¹, ms✝) = [] ∧ ∃ m_better, m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = true
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝¹ h✝¹) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueconstructor
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝

left
¬merge F (ms✝¹, ms✝) = []
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝

right
∃ m_better, m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = true 
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝¹ h✝¹) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase left => 
                
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝

¬merge F (ms✝¹, ms✝) = []apply 
merge_not_empty: ∀ {α : Type} {ms₁ ms₂ : List Meas} {F : Factory α}, ms₁ ≠ [] ∨ ms₂ ≠ [] → merge F (ms₁, ms₂) ≠ []
merge_not_empty
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝

h
ms✝¹ ≠ [] ∨ ms✝ ≠ []
                
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝

¬merge F (ms✝¹, ms✝) = []simp [*]
Goals accomplished! 🐙
              
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝

∃ ms h,
  MeasureSet.union F (MeasureSet.set ms✝¹ h✝¹) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase right => 
                
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝

∃ m_better, m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = truecases 
h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝
h_left'
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝¹: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

h✝: w✝¹ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set w✝¹ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set w✝¹ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

refl
∃ m_better, m_better ∈ merge F (ms✝, w✝¹) ∧ dominates F m_better m = true
                
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝

∃ m_better, m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = truelet ⟨
m_better: Meas
m_better, ⟨
h_mem: m_better ∈ merge F (ms✝, w✝¹)
h_mem, 
h_dom: dominates F m_better m_better✝ = true
h_dom⟩⟩ := 
merge_dom₂: ∀ {α : Type} {F : Factory α} {ms₁ ms₂ : List Meas} {m : Meas},
  pareto F ms₁ → pareto F ms₂ → m ∈ ms₂ → ∃ m_better, m_better ∈ merge F (ms₁, ms₂) ∧ dominates F m_better m = true
merge_dom₂ (
Resolve_pareto: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h_non_empty : ms ≠ []},
  Resolve F d c i (MeasureSet.set ms h_non_empty) → pareto F ms
Resolve_pareto 
h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝¹)
h_left) (
Resolve_pareto: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h_non_empty : ms ≠ []},
  Resolve F d c i (MeasureSet.set ms h_non_empty) → pareto F ms
Resolve_pareto 
h_right: Resolve F d₂ c i (MeasureSet.set w✝¹ h✝)
h_right) 
h_mem_b: m_better ∈ w✝¹
h_mem_b
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝¹: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝¹)

h_mem✝: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better✝: Meas

h_mem_b: m_better✝ ∈ w✝¹

right✝: dominates F m_better✝ m = true

h✝: w✝¹ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set w✝¹ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set w✝¹ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

m_better: Meas

h_mem: m_better ∈ merge F (ms✝, w✝¹)

h_dom: dominates F m_better m_better✝ = true

refl
∃ m_better, m_better ∈ merge F (ms✝, w✝¹) ∧ dominates F m_better m = true
                
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝

∃ m_better, m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = trueexists 
m_better: Meas
m_better
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝¹: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝¹)

h_mem✝: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better✝: Meas

h_mem_b: m_better✝ ∈ w✝¹

right✝: dominates F m_better✝ m = true

h✝: w✝¹ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set w✝¹ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set w✝¹ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

m_better: Meas

h_mem: m_better ∈ merge F (ms✝, w✝¹)

h_dom: dominates F m_better m_better✝ = true

refl
m_better ∈ merge F (ms✝, w✝¹) ∧ dominates F m_better m = true 
                
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝

∃ m_better, m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = truesimp [*]
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝¹: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝¹)

h_mem✝: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better✝: Meas

h_mem_b: m_better✝ ∈ w✝¹

right✝: dominates F m_better✝ m = true

h✝: w✝¹ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set w✝¹ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set w✝¹ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

m_better: Meas

h_mem: m_better ∈ merge F (ms✝, w✝¹)

h_dom: dominates F m_better m_better✝ = true

refl
dominates F m_better m = true
                
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝¹: List Meas

h✝¹: ms✝¹ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝¹ h✝¹)

h_mem: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better: Meas

h_mem_b: m_better ∈ w✝¹

right✝: dominates F m_better m = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set ms✝ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set ms✝ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

h_left': MeasureSet.set ms✝ h✝ = MeasureSet.set w✝¹ w✝

∃ m_better, m_better ∈ merge F (ms✝¹, ms✝) ∧ dominates F m_better m = truedwi { 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝¹: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝¹)

h_mem✝: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better✝: Meas

h_mem_b: m_better✝ ∈ w✝¹

right✝: dominates F m_better✝ m = true

h✝: w✝¹ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set w✝¹ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set w✝¹ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

m_better: Meas

h_mem: m_better ∈ merge F (ms✝, w✝¹)

h_dom: dominates F m_better m_better✝ = true

refl
dominates F m_better m = trueapply 
dominates_trans: ∀ {α : Type} {m₁ m₂ m₃ : Meas} {F : Factory α},
  dominates F m₁ m₂ = true → dominates F m₂ m₃ = true → dominates F m₁ m₃ = true
dominates_trans
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝¹: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝¹)

h_mem✝: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better✝: Meas

h_mem_b: m_better✝ ∈ w✝¹

right✝: dominates F m_better✝ m = true

h✝: w✝¹ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set w✝¹ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set w✝¹ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

m_better: Meas

h_mem: m_better ∈ merge F (ms✝, w✝¹)

h_dom: dominates F m_better m_better✝ = true

refl.h
dominates F m_better ?refl.m₂ = true
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝¹: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝¹)

h_mem✝: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better✝: Meas

h_mem_b: m_better✝ ∈ w✝¹

right✝: dominates F m_better✝ m = true

h✝: w✝¹ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set w✝¹ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set w✝¹ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

m_better: Meas

h_mem: m_better ∈ merge F (ms✝, w✝¹)

h_dom: dominates F m_better m_better✝ = true

refl.h'
dominates F ?refl.m₂ m = true
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

ms✝: List Meas

h✝¹: ms✝ ≠ []

h_left: Resolve F d₁ c i (MeasureSet.set ms✝ h✝¹)

h_mem✝: d_choiceless ∈ L₂✝

w✝¹: List Meas

w✝: w✝¹ ≠ []

m_better✝: Meas

h_mem_b: m_better✝ ∈ w✝¹

right✝: dominates F m_better✝ m = true

h✝: w✝¹ ≠ []

h_right: Resolve F d₂ c i (MeasureSet.set w✝¹ h✝)

this: m.y ≤ F.W →
  m.x ≤ F.W →
    ∃ ms h, MeasureSet.set w✝¹ h✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true

m_better: Meas

h_mem: m_better ∈ merge F (ms✝, w✝¹)

h_dom: dominates F m_better m_better✝ = true

refl.m₂
Meas }
Goals accomplished! 🐙 
    
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_print: Resolve F d c i ml

h_widen: Widen d D

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true| 
Doc.concat: Doc → Doc → Doc
Doc.concat 
d₁: Doc
d₁ 
d₂: Doc
d₂ =>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i ml

h_widen: Widen (Doc.concat d₁ d₂) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_print: Resolve F d c i ml

h_widen: Widen d D

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_widen: Widen (Doc.concat d₁ d₂) D
h_widen
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i ml

L₁✝, L₂✝: List Doc

h₁✝: Widen d₁ L₁✝

h₂✝: Widen d₂ L₂✝

h_mem: d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝)

concat
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true 
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i ml

h_widen: Widen (Doc.concat d₁ d₂) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truerename_i 
h_widen₁: Widen d₁ L₁✝
h_widen₁ 
h_widen₂: Widen d₂ L₂✝
h_widen₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i ml

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝)

concat
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i ml

h_widen: Widen (Doc.concat d₁ d₂) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp at 
h_mem: d_choiceless ∈ List.join (List.map (fun d₁ => List.map (fun d₂ => Doc.concat d₁ d₂) L₂✝) L₁✝)
h_mem
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i ml

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: ∃ a, a ∈ L₁✝ ∧ ∃ a_1, a_1 ∈ L₂✝ ∧ Doc.concat a a_1 = d_choiceless

concat
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i ml

h_widen: Widen (Doc.concat d₁ d₂) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truelet ⟨
d_left: Doc
d_left, 
h_left: d_left ∈ L₁✝
h_left, 
d_right: Doc
d_right, 
h_right: d_right ∈ L₂✝
h_right, 
h_concat: Doc.concat d_left d_right = d_choiceless
h_concat⟩ := 
h_mem: ∃ a, a ∈ L₁✝ ∧ ∃ a_1, a_1 ∈ L₂✝ ∧ Doc.concat a a_1 = d_choiceless
h_mem
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i ml

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

h_mem: ∃ a, a ∈ L₁✝ ∧ ∃ a_1, a_1 ∈ L₂✝ ∧ Doc.concat a a_1 = d_choiceless

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_concat: Doc.concat d_left d_right = d_choiceless

concat
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i ml

h_widen: Widen (Doc.concat d₁ d₂) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueclear 
h_mem: ∃ a, a ∈ L₁✝ ∧ ∃ a_1, a_1 ∈ L₂✝ ∧ Doc.concat a a_1 = d_choiceless
h_mem
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d_choiceless: Doc

m: Meas

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i ml

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_concat: Doc.concat d_left d_right = d_choiceless

concat
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i ml

h_widen: Widen (Doc.concat d₁ d₂) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesubst 
h_concat: Doc.concat d_left d_right = d_choiceless
h_concat
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i ml

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_render: MeasRender F (Doc.concat d_left d_right) c i m

concat
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i ml

h_widen: Widen (Doc.concat d₁ d₂) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_print: Resolve F (Doc.concat d₁ d₂) c i ml
h_print
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_render: MeasRender F (Doc.concat d_left d_right) c i m

m✝: Meas

ms'✝: MeasureSet

m'✝: Meas

h_taint✝: MeasureSet.taint ms'✝ = MeasureSet.tainted m'✝

h_right✝: Resolve F d₂ m✝.last i ms'✝

h_left✝: Resolve F d₁ c i (MeasureSet.tainted m✝)

concat.concat_taint
∃ ms h,
  MeasureSet.tainted (Meas.concat F m✝ m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_render: MeasRender F (Doc.concat d_left d_right) c i m

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h_left✝: Resolve F d₁ c i (MeasureSet.set ms✝ h_non_empty✝)

h✝: ResolveConcat F ms✝ d₂ i ml

concat.concat_set
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i ml

h_widen: Widen (Doc.concat d₁ d₂) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase concat_taint 
h_taint: MeasureSet.taint ms'✝ = MeasureSet.tainted m'✝
h_taint 
h_right': Resolve F d₂ m✝.last i ms'✝
h_right' 
h_left': Resolve F d₁ c i (MeasureSet.tainted m✝)
h_left' => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_render: MeasRender F (Doc.concat d_left d_right) c i m

m✝: Meas

ms'✝: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms'✝ = MeasureSet.tainted m'✝

h_right': Resolve F d₂ m✝.last i ms'✝

h_left': Resolve F d₁ c i (MeasureSet.tainted m✝)

∃ ms h,
  MeasureSet.tainted (Meas.concat F m✝ m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_render: MeasRender F (Doc.concat d_left d_right) c i m
h_render
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

m✝: Meas

ms'✝: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms'✝ = MeasureSet.tainted m'✝

h_right': Resolve F d₂ m✝.last i ms'✝

h_left': Resolve F d₁ c i (MeasureSet.tainted m✝)

m₁✝, m₂✝: Meas

h₂✝: MeasRender F d_right m₁✝.last i m₂✝

h₁✝: MeasRender F d_left c i m₁✝

h✝: m = Meas.concat F m₁✝ m₂✝

concat
∃ ms h,
  MeasureSet.tainted (Meas.concat F m✝ m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_render: MeasRender F (Doc.concat d_left d_right) c i m

m✝: Meas

ms'✝: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms'✝ = MeasureSet.tainted m'✝

h_right': Resolve F d₂ m✝.last i ms'✝

h_left': Resolve F d₁ c i (MeasureSet.tainted m✝)

∃ ms h,
  MeasureSet.tainted (Meas.concat F m✝ m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truerename_i 
hh_right: MeasRender F d_right m₁✝.last i m₂✝
hh_right 
hh_left: MeasRender F d_left c i m₁✝
hh_left 
hh: m = Meas.concat F m₁✝ m₂✝
hh
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

m✝: Meas

ms'✝: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms'✝ = MeasureSet.tainted m'✝

h_right': Resolve F d₂ m✝.last i ms'✝

h_left': Resolve F d₁ c i (MeasureSet.tainted m✝)

m₁✝, m₂✝: Meas

hh_right: MeasRender F d_right m₁✝.last i m₂✝

hh_left: MeasRender F d_left c i m₁✝

hh: m = Meas.concat F m₁✝ m₂✝

concat
∃ ms h,
  MeasureSet.tainted (Meas.concat F m✝ m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_render: MeasRender F (Doc.concat d_left d_right) c i m

m✝: Meas

ms'✝: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms'✝ = MeasureSet.tainted m'✝

h_right': Resolve F d₂ m✝.last i ms'✝

h_left': Resolve F d₁ c i (MeasureSet.tainted m✝)

∃ ms h,
  MeasureSet.tainted (Meas.concat F m✝ m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesubst 
hh: m = Meas.concat F m₁✝ m₂✝
hh
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

m✝: Meas

ms'✝: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms'✝ = MeasureSet.tainted m'✝

h_right': Resolve F d₂ m✝.last i ms'✝

h_left': Resolve F d₁ c i (MeasureSet.tainted m✝)

m₁✝, m₂✝: Meas

hh_right: MeasRender F d_right m₁✝.last i m₂✝

hh_left: MeasRender F d_left c i m₁✝

h_y: (Meas.concat F m₁✝ m₂✝).y ≤ F.W

h_x: (Meas.concat F m₁✝ m₂✝).x ≤ F.W

concat
∃ ms h,
  MeasureSet.tainted (Meas.concat F m✝ m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁✝ m₂✝) = true
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_render: MeasRender F (Doc.concat d_left d_right) c i m

m✝: Meas

ms'✝: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms'✝ = MeasureSet.tainted m'✝

h_right': Resolve F d₂ m✝.last i ms'✝

h_left': Resolve F d₁ c i (MeasureSet.tainted m✝)

∃ ms h,
  MeasureSet.tainted (Meas.concat F m✝ m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp [
Meas.concat: {α : Type} → Factory α → Meas → Meas → Meas
Meas.concat] at 
h_y: (Meas.concat F m₁✝ m₂✝).y ≤ F.W
h_y 
h_x: (Meas.concat F m₁✝ m₂✝).x ≤ F.W
h_x
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

m✝: Meas

ms'✝: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms'✝ = MeasureSet.tainted m'✝

h_right': Resolve F d₂ m✝.last i ms'✝

h_left': Resolve F d₁ c i (MeasureSet.tainted m✝)

m₁✝, m₂✝: Meas

hh_right: MeasRender F d_right m₁✝.last i m₂✝

hh_left: MeasRender F d_left c i m₁✝

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

concat
∃ ms h,
  MeasureSet.tainted (Meas.concat F m✝ m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁✝ m₂✝) = true
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_render: MeasRender F (Doc.concat d_left d_right) c i m

m✝: Meas

ms'✝: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms'✝ = MeasureSet.tainted m'✝

h_right': Resolve F d₂ m✝.last i ms'✝

h_left': Resolve F d₁ c i (MeasureSet.tainted m✝)

∃ ms h,
  MeasureSet.tainted (Meas.concat F m✝ m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truelet ⟨
_: List Meas
_, 
_: w✝¹ ≠ []
_, _, _⟩ := 
Resolve_optimal: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ml : MeasureSet} {D : List Doc} {d_choiceless : Doc} {m : Meas},
  Resolve F d c i ml →
    Widen d D →
      d_choiceless ∈ D →
        MeasRender F d_choiceless c i m →
          m.y ≤ F.W →
            m.x ≤ F.W → ∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
Resolve_optimal 
h_left': Resolve F d₁ c i (MeasureSet.tainted m✝)
h_left' 
h_widen₁: Widen d₁ L₁✝
h_widen₁ 
h_left: d_left ∈ L₁✝
h_left 
hh_left: MeasRender F d_left c i m₁✝
hh_left 
h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W
h_y.
left: ∀ {a b : Prop}, a ∧ b → a
left 
h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W
h_x.
left: ∀ {a b : Prop}, a ∧ b → a
left
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

m✝: Meas

ms'✝: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms'✝ = MeasureSet.tainted m'✝

h_right': Resolve F d₂ m✝.last i ms'✝

h_left': Resolve F d₁ c i (MeasureSet.tainted m✝)

m₁✝, m₂✝: Meas

hh_right: MeasRender F d_right m₁✝.last i m₂✝

hh_left: MeasRender F d_left c i m₁✝

h_y: m₁✝.y ≤ F.W ∧ m₂✝.y ≤ F.W

h_x: m₁✝.x ≤ F.W ∧ m₂✝.x ≤ F.W

w✝¹: List Meas

w✝: w✝¹ ≠ []

left✝: MeasureSet.tainted m✝ = MeasureSet.set w✝¹ w✝

right✝: ∃ m_better, m_better ∈ w✝¹ ∧ dominates F m_better m₁✝ = true

concat
∃ ms h,
  MeasureSet.tainted (Meas.concat F m✝ m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁✝ m₂✝) = true
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_render: MeasRender F (Doc.concat d_left d_right) c i m

m✝: Meas

ms'✝: MeasureSet

m'✝: Meas

h_taint: MeasureSet.taint ms'✝ = MeasureSet.tainted m'✝

h_right': Resolve F d₂ m✝.last i ms'✝

h_left': Resolve F d₁ c i (MeasureSet.tainted m✝)

∃ ms h,
  MeasureSet.tainted (Meas.concat F m✝ m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecontradiction
Goals accomplished! 🐙
      
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

D: List Doc

d_choiceless: Doc

m: Meas

h_mem: d_choiceless ∈ D

h_render: MeasRender F d_choiceless c i m

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

h_print: Resolve F (Doc.concat d₁ d₂) c i ml

h_widen: Widen (Doc.concat d₁ d₂) D

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecase concat_set 
ms: List Meas
ms 
h_non_empty: ms ≠ []
h_non_empty 
h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)
h_left' 
h_right': ResolveConcat F ms d₂ i ml
h_right' => 
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_render: MeasRender F (Doc.concat d_left d_right) c i m

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_render: MeasRender F (Doc.concat d_left d_right) c i m
h_render
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁✝, m₂✝: Meas

h₂✝: MeasRender F d_right m₁✝.last i m₂✝

h₁✝: MeasRender F d_left c i m₁✝

h✝: m = Meas.concat F m₁✝ m₂✝

concat
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_render: MeasRender F (Doc.concat d_left d_right) c i m

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truerename_i 
m₁: Meas
m₁ 
m₂: Meas
m₂ 
hh_right: MeasRender F d_right m₁.last i m₂
hh_right 
hh_left: MeasRender F d_left c i m₁
hh_left 
hh: m = Meas.concat F m₁ m₂
hh
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

hh: m = Meas.concat F m₁ m₂

concat
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_render: MeasRender F (Doc.concat d_left d_right) c i m

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesubst 
hh: m = Meas.concat F m₁ m₂
hh
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_y: (Meas.concat F m₁ m₂).y ≤ F.W

h_x: (Meas.concat F m₁ m₂).x ≤ F.W

concat
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_render: MeasRender F (Doc.concat d_left d_right) c i m

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truesimp [
Meas.concat: {α : Type} → Factory α → Meas → Meas → Meas
Meas.concat] at 
h_x: (Meas.concat F m₁ m₂).x ≤ F.W
h_x 
h_y: (Meas.concat F m₁ m₂).y ≤ F.W
h_y
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

concat
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_render: MeasRender F (Doc.concat d_left d_right) c i m

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truelet ⟨
ms_left: List Meas
ms_left, 
h_mem_left: ms_left ≠ []
h_mem_left, 
h_eq: MeasureSet.set ms h_non_empty = MeasureSet.set ms_left h_mem_left
h_eq, 
m_better: Meas
m_better, 
h_mem': m_better ∈ ms_left
h_mem', 
h_dom: dominates F m_better m₁ = true
h_dom⟩ := 
Resolve_optimal: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ml : MeasureSet} {D : List Doc} {d_choiceless : Doc} {m : Meas},
  Resolve F d c i ml →
    Widen d D →
      d_choiceless ∈ D →
        MeasRender F d_choiceless c i m →
          m.y ≤ F.W →
            m.x ≤ F.W → ∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
Resolve_optimal 
h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)
h_left' 
h_widen₁: Widen d₁ L₁✝
h_widen₁ 
h_left: d_left ∈ L₁✝
h_left 
hh_left: MeasRender F d_left c i m₁
hh_left 
h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W
h_y.
left: ∀ {a b : Prop}, a ∧ b → a
left 
h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W
h_x.
left: ∀ {a b : Prop}, a ∧ b → a
left
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

ms_left: List Meas

h_mem_left: ms_left ≠ []

h_eq: MeasureSet.set ms h_non_empty = MeasureSet.set ms_left h_mem_left

m_better: Meas

h_mem': m_better ∈ ms_left

h_dom: dominates F m_better m₁ = true

concat
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_render: MeasRender F (Doc.concat d_left d_right) c i m

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = truecases 
h_eq: MeasureSet.set ms h_non_empty = MeasureSet.set ms_left h_mem_left
h_eq
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
        
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

m: Meas

h_y: m.y ≤ F.W

h_x: m.x ≤ F.W

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

h_render: MeasRender F (Doc.concat d_left d_right) c i m

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = trueapply 
ResolveConcat_optimal: ∀ {α : Type} {F : Factory α} {ms : List Meas} {d₂ : Doc} {i : ℕ} {ml : MeasureSet} {L₂ : List Doc} {d_right : Doc}
  {m₂ m_better_left m₁ : Meas},
  ResolveConcat F ms d₂ i ml →
    Widen d₂ L₂ →
      d_right ∈ L₂ →
        MeasRender F d_right m₁.last i m₂ →
          m₁.x ≤ F.W ∧ m₂.x ≤ F.W →
            m₁.y ≤ F.W ∧ m₂.y ≤ F.W →
              dominates F m_better_left m₁ = true →
                m_better_left ∈ ms →
                  ∃ ms h,
                    ml = MeasureSet.set ms h ∧                       ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
ResolveConcat_optimal
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.h_print
ResolveConcat F ?concat.refl.ms ?concat.refl.d₂ ?concat.refl.i ml
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.h_widen
Widen ?concat.refl.d₂ ?concat.refl.L₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.h_choiceless
?concat.refl.d_right ∈ ?concat.refl.L₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.h_render
MeasRender F ?concat.refl.d_right m₁.last ?concat.refl.i m₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.h_x
m₁.x ≤ F.W ∧ m₂.x ≤ F.W
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.h_y
m₁.y ≤ F.W ∧ m₂.y ≤ F.W
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.h_dom
dominates F ?concat.refl.m_better_left m₁ = true
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.h_mem
?concat.refl.m_better_left ∈ ?concat.refl.ms
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.ms
List Meas
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.d₂
Doc
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.i
ℕ
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.L₂
List Doc
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.d_right
Doc
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.m_better_left
Meas 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true<;>
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.h_print
ResolveConcat F ?concat.refl.ms ?concat.refl.d₂ ?concat.refl.i ml
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.h_widen
Widen ?concat.refl.d₂ ?concat.refl.L₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.h_choiceless
?concat.refl.d_right ∈ ?concat.refl.L₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.h_render
MeasRender F ?concat.refl.d_right m₁.last ?concat.refl.i m₂
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.h_x
m₁.x ≤ F.W ∧ m₂.x ≤ F.W
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.h_y
m₁.y ≤ F.W ∧ m₂.y ≤ F.W
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.h_dom
dominates F ?concat.refl.m_better_left m₁ = true
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.h_mem
?concat.refl.m_better_left ∈ ?concat.refl.ms
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.ms
List Meas
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.d₂
Doc
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.i
ℕ
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.L₂
List Doc
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.d_right
Doc
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl.m_better_left
Meas 
α✝: Type

F: Factory α✝

d: Doc

c, i: ℕ

ml: MeasureSet

d₁, d₂: Doc

L₁✝, L₂✝: List Doc

h_widen₁: Widen d₁ L₁✝

h_widen₂: Widen d₂ L₂✝

d_left: Doc

h_left: d_left ∈ L₁✝

d_right: Doc

h_right: d_right ∈ L₂✝

ms: List Meas

h_non_empty: ms ≠ []

h_left': Resolve F d₁ c i (MeasureSet.set ms h_non_empty)

h_right': ResolveConcat F ms d₂ i ml

m₁, m₂: Meas

hh_right: MeasRender F d_right m₁.last i m₂

hh_left: MeasRender F d_left c i m₁

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

m_better: Meas

h_dom: dominates F m_better m₁ = true

h_mem_left: ms ≠ []

h_mem': m_better ∈ ms

concat.refl
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueassumption
Goals accomplished! 🐙
    
  theorem 
ResolveConcat_optimal: ∀ {α : Type} {F : Factory α} {ms : List Meas} {d₂ : Doc} {i : ℕ} {ml : MeasureSet} {L₂ : List Doc} {d_right : Doc}
  {m₂ m_better_left m₁ : Meas},
  ResolveConcat F ms d₂ i ml →
    Widen d₂ L₂ →
      d_right ∈ L₂ →
        MeasRender F d_right m₁.last i m₂ →
          m₁.x ≤ F.W ∧ m₂.x ≤ F.W →
            m₁.y ≤ F.W ∧ m₂.y ≤ F.W →
              dominates F m_better_left m₁ = true →
                m_better_left ∈ ms →
                  ∃ ms h,
                    ml = MeasureSet.set ms h ∧                       ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
ResolveConcat_optimal
      (
h_print: ResolveConcat F ms d₂ i ml
h_print: 
ResolveConcat: {α : Type} → Factory α → List Meas → Doc → ℕ → MeasureSet → Prop
ResolveConcat 
F: ?m.309
F 
ms: ?m.316
ms 
d₂: ?m.323
d₂ 
i: ?m.329
i 
ml: ?m.335
ml)
      (
h_widen: Widen d₂ L₂
h_widen: 
Widen: Doc → List Doc → Prop
Widen 
d₂: ?m.323
d₂ 
L₂: ?m.344
L₂)
      (
h_choiceless: d_right ∈ L₂
h_choiceless: 
d_right: ?m.369
d_right ∈ 
L₂: ?m.344
L₂)
      (
h_render: MeasRender F d_right (sorryAx ℕ true) i m₂
h_render: 
MeasRender: {α : Type} → Factory α → Doc → ℕ → ℕ → Meas → Prop
MeasRender 
F: ?m.309
F 
d_right: ?m.369
d_right 
m₁: ?m.554
m₁
m₁.last: ℕ
.
last: {α : Type} → Meas → ℕ
last 
i: ?m.329
i 
m₂: ?m.408
m₂)
      (
h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W
h_x: 
m₁: ?m.554
m₁
m₁.x: unknown metavariable '?_uniq.522'
.
x: {α : Type} → Meas → ℕ
x ≤ 
F: ?m.309
F.
W: {α : Type} → Factory α → ℕ
W ∧ 
m₂: ?m.408
m₂.
x: {α : Type} → Meas → ℕ
x ≤ 
F: ?m.309
F.
W: {α : Type} → Factory α → ℕ
W)
      (
h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W
h_y: 
m₁: ?m.554
m₁
m₁.y: unknown metavariable '?_uniq.538'
.
y: {α : Type} → Meas → ℕ
y ≤ 
F: ?m.309
F.
W: {α : Type} → Factory α → ℕ
W ∧ 
m₂: ?m.408
m₂.
y: {α : Type} → Meas → ℕ
y ≤ 
F: ?m.309
F.
W: {α : Type} → Factory α → ℕ
W)
      (
h_dom: dominates F m_better_left m₁ = true
h_dom: 
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates 
F: ?m.309
F 
m_better_left: ?m.483
m_better_left 
m₁: ?m.554
m₁)
      (
h_mem: m_better_left ∈ ms
h_mem: 
m_better_left: ?m.483
m_better_left ∈ 
ms: ?m.316
ms) :
         ∃ 
ms: ?m.669
ms 
h: ?m.674
h, 
ml: ?m.335
ml = 
MeasureSet.set: {α : Type} → (ms : List Meas) → ms ≠ [] → MeasureSet
MeasureSet.set 
ms: ?m.669
ms 
h: ?m.674
h ∧ ∃ 
m_better: ?m.708
m_better, 
m_better: ?m.708
m_better ∈ 
ms: ?m.669
ms ∧ 
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates 
F: ?m.309
F 
m_better: ?m.708
m_better (
Meas.concat: {α : Type} → Factory α → Meas → Meas → Meas
Meas.concat 
F: ?m.309
F 
m₁: ?m.554
m₁ 
m₂: ?m.408
m₂) := by
Goals accomplished! 🐙 
  
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ml: MeasureSet

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_print: ResolveConcat F ms d₂ i ml

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

h_mem: m_better_left ∈ ms

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecases 
h_print: ResolveConcat F ms d₂ i ml
h_print
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

ml: MeasureSet

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

m✝: Meas

h_mem: m_better_left ∈ [m✝]

h_current✝: ResolveConcatOne F d₂ m✝ i ml

one
∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr✝: MeasureSet

m✝: Meas

msr'✝: MeasureSet

h_mem: m_better_left ∈ m✝ :: ms✝

h_rest✝: ResolveConcat F ms✝ d₂ i msr✝

h_current✝: ResolveConcatOne F d₂ m✝ i msr'✝

cons
∃ ms h,
  MeasureSet.union F msr'✝ msr✝ = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true 
  
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ml: MeasureSet

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_print: ResolveConcat F ms d₂ i ml

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

h_mem: m_better_left ∈ ms

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecase one 
h_print: ResolveConcatOne F d₂ m✝ i ml
h_print => 
    
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

ml: MeasureSet

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

m✝: Meas

h_mem: m_better_left ∈ [m✝]

h_print: ResolveConcatOne F d₂ m✝ i ml

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truesimp at 
h_mem: m_better_left ∈ [m✝]
h_mem
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

ml: MeasureSet

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

m✝: Meas

h_print: ResolveConcatOne F d₂ m✝ i ml

h_mem: m_better_left = m✝

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
    
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

ml: MeasureSet

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

m✝: Meas

h_mem: m_better_left ∈ [m✝]

h_print: ResolveConcatOne F d₂ m✝ i ml

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truesubst 
h_mem: m_better_left = m✝
h_mem
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

ml: MeasureSet

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

h_print: ResolveConcatOne F d₂ m_better_left i ml

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
    
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

ml: MeasureSet

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

m✝: Meas

h_mem: m_better_left ∈ [m✝]

h_print: ResolveConcatOne F d₂ m✝ i ml

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueexact 
ResolveConcatOne_optimal: ∀ {d₂ : Doc} {L₂ : List Doc} {d_right : Doc} {α : Type} {F : Factory α} {m_better : Meas} {i : ℕ} {ml : MeasureSet}
  {m₂ m₁ : Meas},
  Widen d₂ L₂ →
    d_right ∈ L₂ →
      ResolveConcatOne F d₂ m_better i ml →
        MeasRender F d_right m₁.last i m₂ →
          m₁.x ≤ F.W ∧ m₂.x ≤ F.W →
            m₁.y ≤ F.W ∧ m₂.y ≤ F.W →
              dominates F m_better m₁ = true →
                ∃ ms h,
                  ml = MeasureSet.set ms h ∧                     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
ResolveConcatOne_optimal 
h_widen: Widen d₂ L₂
h_widen 
h_choiceless: d_right ∈ L₂
h_choiceless 
h_print: ResolveConcatOne F d₂ m_better_left i ml
h_print 
h_render: MeasRender F d_right m₁.last i m₂
h_render 
h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W
h_x 
h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W
h_y 
h_dom: dominates F m_better_left m₁ = true
h_dom
Goals accomplished! 🐙 
  
α✝: Type

F: Factory α✝

ms: List Meas

d₂: Doc

i: ℕ

ml: MeasureSet

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_print: ResolveConcat F ms d₂ i ml

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

h_mem: m_better_left ∈ ms

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecase cons 
msr': MeasureSet
msr' 
the_m: Meas
the_m 
msr: MeasureSet
msr 
h_rest: ResolveConcat F ms✝ d₂ i msr'
h_rest 
h_print: ResolveConcatOne F d₂ the_m i msr
h_print => 
    
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr': MeasureSet

the_m: Meas

msr: MeasureSet

h_mem: m_better_left ∈ the_m :: ms✝

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ the_m i msr

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecases 
h_mem: m_better_left ∈ the_m :: ms✝
h_mem
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr', msr: MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ m_better_left i msr

head
∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr': MeasureSet

the_m: Meas

msr: MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ the_m i msr

a✝: List.Mem m_better_left ms✝

tail
∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true 
    
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr': MeasureSet

the_m: Meas

msr: MeasureSet

h_mem: m_better_left ∈ the_m :: ms✝

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ the_m i msr

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecase head => 
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr', msr: MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ m_better_left i msr

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truehave := 
ResolveConcatOne_optimal: ∀ {d₂ : Doc} {L₂ : List Doc} {d_right : Doc} {α : Type} {F : Factory α} {m_better : Meas} {i : ℕ} {ml : MeasureSet}
  {m₂ m₁ : Meas},
  Widen d₂ L₂ →
    d_right ∈ L₂ →
      ResolveConcatOne F d₂ m_better i ml →
        MeasRender F d_right m₁.last i m₂ →
          m₁.x ≤ F.W ∧ m₂.x ≤ F.W →
            m₁.y ≤ F.W ∧ m₂.y ≤ F.W →
              dominates F m_better m₁ = true →
                ∃ ms h,
                  ml = MeasureSet.set ms h ∧                     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
ResolveConcatOne_optimal 
h_widen: Widen d₂ L₂
h_widen 
h_choiceless: d_right ∈ L₂
h_choiceless 
h_print: ResolveConcatOne F d₂ m_better_left i msr
h_print 
h_render: MeasRender F d_right m₁.last i m₂
h_render 
h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W
h_x 
h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W
h_y 
h_dom: dominates F m_better_left m₁ = true
h_dom
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr', msr: MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ m_better_left i msr

this: ∃ ms h, msr = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true 
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr', msr: MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ m_better_left i msr

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truelet ⟨
ms: List Meas
ms, 
_: ms ≠ []
_, 
h_eq: msr = MeasureSet.set ms w✝
h_eq, 
h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
h_other⟩ := 
this: ?m.174068
this
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr', msr: MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ m_better_left i msr

this: ∃ ms h, msr = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms: List Meas

w✝: ms ≠ []

h_eq: msr = MeasureSet.set ms w✝

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr', msr: MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ m_better_left i msr

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truesubst 
h_eq: msr = MeasureSet.set ms w✝
h_eq
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr': MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms w✝) msr' = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true 
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr', msr: MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ m_better_left i msr

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecases 
msr': MeasureSet
msr'
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

tainted
∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms w✝) (MeasureSet.tainted m✝) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

set
∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms w✝) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr', msr: MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ m_better_left i msr

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecase tainted => 
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms w✝) (MeasureSet.tainted m✝) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueexists 
ms: List Meas
ms, (
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms w✝) (MeasureSet.tainted m✝) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueby
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

m✝: Meas

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.tainted m✝)

ms ≠ []simp [*]
Goals accomplished! 🐙)
Goals accomplished! 🐙
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr', msr: MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ m_better_left i msr

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecase set => 
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms w✝) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truehave 
h_pareto: ?m.179846
h_pareto := 
ResolveConcatOne_pareto: ∀ {α : Type} {F : Factory α} {d : Doc} {m : Meas} {i : ℕ} {msr : List Meas} {h_non_empty : msr ≠ []},
  ResolveConcatOne F d m i (MeasureSet.set msr h_non_empty) → pareto F msr
ResolveConcatOne_pareto 
h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)
h_print
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms w✝) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true 
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms w✝) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truehave 
h_pareto': ?m.179867
h_pareto' := 
ResolveConcat_pareto: ∀ {α : Type} {F : Factory α} {ms : List Meas} {d : Doc} {i : ℕ} {msr : List Meas} {h_non_empty : msr ≠ []},
  ResolveConcat F ms d i (MeasureSet.set msr h_non_empty) → pareto F msr
ResolveConcat_pareto 
h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)
h_rest
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms w✝) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms w✝) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truesimp [
MeasureSet.union: {α : Type} → Factory α → MeasureSet → MeasureSet → MeasureSet
MeasureSet.union]
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

¬merge F (ms, ms✝) = [] ∧ ∃ m_better, m_better ∈ merge F (ms, ms✝) ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms w✝) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueconstructor
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

left
¬merge F (ms, ms✝) = []
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

right
∃ m_better, m_better ∈ merge F (ms, ms✝) ∧ dominates F m_better (Meas.concat F m₁ m₂) = true 
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms w✝) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecase left => 
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

¬merge F (ms, ms✝) = []apply 
merge_not_empty: ∀ {α : Type} {ms₁ ms₂ : List Meas} {F : Factory α}, ms₁ ≠ [] ∨ ms₂ ≠ [] → merge F (ms₁, ms₂) ≠ []
merge_not_empty
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

h
ms ≠ [] ∨ ms✝ ≠ [] 
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

¬merge F (ms, ms✝) = []simp [*]
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms w✝) (MeasureSet.set ms✝ h✝) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecase right => 
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

∃ m_better, m_better ∈ merge F (ms, ms✝) ∧ dominates F m_better (Meas.concat F m₁ m₂) = truelet ⟨
m: Meas
m, 
hh: m ∈ ms ∧ dominates F m (Meas.concat F m₁ m₂) = true
hh⟩ := 
h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
h_other
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

m: Meas

hh: m ∈ ms ∧ dominates F m (Meas.concat F m₁ m₂) = true

∃ m_better, m_better ∈ merge F (ms, ms✝) ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

∃ m_better, m_better ∈ merge F (ms, ms✝) ∧ dominates F m_better (Meas.concat F m₁ m₂) = truelet ⟨
mm: Meas
mm, 
hhh: mm ∈ merge F (ms, ms✝) ∧ dominates F mm m = true
hhh⟩ := 
merge_dom₁: ∀ {α : Type} {F : Factory α} {ms₁ ms₂ : List Meas} {m : Meas},
  pareto F ms₁ → pareto F ms₂ → m ∈ ms₁ → ∃ m_better, m_better ∈ merge F (ms₁, ms₂) ∧ dominates F m_better m = true
merge_dom₁ 
h_pareto: ?m.179846
h_pareto 
h_pareto': ?m.179867
h_pareto' 
hh: m ∈ ms ∧ dominates F m (Meas.concat F m₁ m₂) = true
hh.
left: ∀ {a b : Prop}, a ∧ b → a
left
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

m: Meas

hh: m ∈ ms ∧ dominates F m (Meas.concat F m₁ m₂) = true

mm: Meas

hhh: mm ∈ merge F (ms, ms✝) ∧ dominates F mm m = true

∃ m_better, m_better ∈ merge F (ms, ms✝) ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

∃ m_better, m_better ∈ merge F (ms, ms✝) ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueexists 
mm: Meas
mm
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

m: Meas

hh: m ∈ ms ∧ dominates F m (Meas.concat F m₁ m₂) = true

mm: Meas

hhh: mm ∈ merge F (ms, ms✝) ∧ dominates F mm m = true

mm ∈ merge F (ms, ms✝) ∧ dominates F mm (Meas.concat F m₁ m₂) = true 
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

∃ m_better, m_better ∈ merge F (ms, ms✝) ∧ dominates F m_better (Meas.concat F m₁ m₂) = truesimp [
hhh: mm ∈ merge F (ms, ms✝) ∧ dominates F mm m = true
hhh]
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

m: Meas

hh: m ∈ ms ∧ dominates F m (Meas.concat F m₁ m₂) = true

mm: Meas

hhh: mm ∈ merge F (ms, ms✝) ∧ dominates F mm m = true

dominates F mm (Meas.concat F m₁ m₂) = true
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

∃ m_better, m_better ∈ merge F (ms, ms✝) ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueapply 
dominates_trans: ∀ {α : Type} {m₁ m₂ m₃ : Meas} {F : Factory α},
  dominates F m₁ m₂ = true → dominates F m₂ m₃ = true → dominates F m₁ m₃ = true
dominates_trans
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

m: Meas

hh: m ∈ ms ∧ dominates F m (Meas.concat F m₁ m₂) = true

mm: Meas

hhh: mm ∈ merge F (ms, ms✝) ∧ dominates F mm m = true

h
dominates F mm ?m₂ = true
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

m: Meas

hh: m ∈ ms ∧ dominates F m (Meas.concat F m₁ m₂) = true

mm: Meas

hhh: mm ∈ merge F (ms, ms✝) ∧ dominates F mm m = true

h'
dominates F ?m₂ (Meas.concat F m₁ m₂) = true
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

m: Meas

hh: m ∈ ms ∧ dominates F m (Meas.concat F m₁ m₂) = true

mm: Meas

hhh: mm ∈ merge F (ms, ms✝) ∧ dominates F mm m = true

m₂
Meas 
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

∃ m_better, m_better ∈ merge F (ms, ms✝) ∧ dominates F m_better (Meas.concat F m₁ m₂) = true. 
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

m: Meas

hh: m ∈ ms ∧ dominates F m (Meas.concat F m₁ m₂) = true

mm: Meas

hhh: mm ∈ merge F (ms, ms✝) ∧ dominates F mm m = true

h
dominates F mm ?m₂ = true
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

m: Meas

hh: m ∈ ms ∧ dominates F m (Meas.concat F m₁ m₂) = true

mm: Meas

hhh: mm ∈ merge F (ms, ms✝) ∧ dominates F mm m = true

h'
dominates F ?m₂ (Meas.concat F m₁ m₂) = true
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

m: Meas

hh: m ∈ ms ∧ dominates F m (Meas.concat F m₁ m₂) = true

mm: Meas

hhh: mm ∈ merge F (ms, ms✝) ∧ dominates F mm m = true

m₂
Measapply 
hhh: mm ∈ merge F (ms, ms✝) ∧ dominates F mm m = true
hhh.
right: ∀ {a b : Prop}, a ∧ b → b
right
Goals accomplished! 🐙 
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

∃ m_better, m_better ∈ merge F (ms, ms✝) ∧ dominates F m_better (Meas.concat F m₁ m₂) = true. 
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹, ms: List Meas

w✝: ms ≠ []

h_other: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_print: ResolveConcatOne F d₂ m_better_left i (MeasureSet.set ms w✝)

this: ∃ ms_1 h,
  MeasureSet.set ms w✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

ms✝: List Meas

h✝: ms✝ ≠ []

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms

h_pareto': pareto F ms✝

m: Meas

hh: m ∈ ms ∧ dominates F m (Meas.concat F m₁ m₂) = true

mm: Meas

hhh: mm ∈ merge F (ms, ms✝) ∧ dominates F mm m = true

h'
dominates F m (Meas.concat F m₁ m₂) = trueapply 
hh: m ∈ ms ∧ dominates F m (Meas.concat F m₁ m₂) = true
hh.
right: ∀ {a b : Prop}, a ∧ b → b
right
Goals accomplished! 🐙
    
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr': MeasureSet

the_m: Meas

msr: MeasureSet

h_mem: m_better_left ∈ the_m :: ms✝

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ the_m i msr

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecase tail 
h_mem: List.Mem m_better_left ms✝
h_mem =>
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr': MeasureSet

the_m: Meas

msr: MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ the_m i msr

h_mem: List.Mem m_better_left ms✝

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truelet ⟨
ms: List Meas
ms, 
h_non_empty: ms ≠ []
h_non_empty, 
h₁: msr' = MeasureSet.set ms h_non_empty
h₁, 
h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
h₂⟩ := 
ResolveConcat_optimal: ∀ {α : Type} {F : Factory α} {ms : List Meas} {d₂ : Doc} {i : ℕ} {ml : MeasureSet} {L₂ : List Doc} {d_right : Doc}
  {m₂ m_better_left m₁ : Meas},
  ResolveConcat F ms d₂ i ml →
    Widen d₂ L₂ →
      d_right ∈ L₂ →
        MeasRender F d_right m₁.last i m₂ →
          m₁.x ≤ F.W ∧ m₂.x ≤ F.W →
            m₁.y ≤ F.W ∧ m₂.y ≤ F.W →
              dominates F m_better_left m₁ = true →
                m_better_left ∈ ms →
                  ∃ ms h,
                    ml = MeasureSet.set ms h ∧                       ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
ResolveConcat_optimal 
h_rest: ResolveConcat F ms✝ d₂ i msr'
h_rest 
h_widen: Widen d₂ L₂
h_widen 
h_choiceless: d_right ∈ L₂
h_choiceless 
h_render: MeasRender F d_right m₁.last i m₂
h_render 
h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W
h_x 
h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W
h_y 
h_dom: dominates F m_better_left m₁ = true
h_dom 
h_mem: List.Mem m_better_left ms✝
h_mem
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr': MeasureSet

the_m: Meas

msr: MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ the_m i msr

h_mem: List.Mem m_better_left ms✝

ms: List Meas

h_non_empty: ms ≠ []

h₁: msr' = MeasureSet.set ms h_non_empty

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr': MeasureSet

the_m: Meas

msr: MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ the_m i msr

h_mem: List.Mem m_better_left ms✝

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truesubst 
h₁: msr' = MeasureSet.set ms h_non_empty
h₁
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

the_m: Meas

msr: MeasureSet

h_print: ResolveConcatOne F d₂ the_m i msr

h_mem: List.Mem m_better_left ms✝

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h_non_empty)

∃ ms_1 h,
  MeasureSet.union F msr (MeasureSet.set ms h_non_empty) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true 
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr': MeasureSet

the_m: Meas

msr: MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ the_m i msr

h_mem: List.Mem m_better_left ms✝

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecases 
msr: MeasureSet
msr
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h_non_empty)

m✝: Meas

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.tainted m✝)

tainted
∃ ms_1 h,
  MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms h_non_empty) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

set
∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms h_non_empty) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true 
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr': MeasureSet

the_m: Meas

msr: MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ the_m i msr

h_mem: List.Mem m_better_left ms✝

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecase tainted => 
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h_non_empty)

m✝: Meas

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.tainted m✝)

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms h_non_empty) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecases 
h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.tainted m✝)
h_print
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h_non_empty)

m'✝: Meas

h✝: Resolve F d₂ the_m.last i (MeasureSet.tainted m'✝)

tainted
∃ ms_1 h,
  MeasureSet.union F (MeasureSet.tainted (Meas.concat F the_m m'✝)) (MeasureSet.set ms h_non_empty) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true 
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝ d₂ i (MeasureSet.set ms h_non_empty)

m✝: Meas

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.tainted m✝)

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.tainted m✝) (MeasureSet.set ms h_non_empty) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truesimp [
MeasureSet.union: {α : Type} → Factory α → MeasureSet → MeasureSet → MeasureSet
MeasureSet.union, 
h_non_empty: ms ≠ []
h_non_empty, 
h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
h₂]
Goals accomplished! 🐙
      
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝: List Meas

msr': MeasureSet

the_m: Meas

msr: MeasureSet

h_rest: ResolveConcat F ms✝ d₂ i msr'

h_print: ResolveConcatOne F d₂ the_m i msr

h_mem: List.Mem m_better_left ms✝

∃ ms h,
  MeasureSet.union F msr msr' = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecase set => 
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms h_non_empty) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truehave 
h_pareto: ?m.192230
h_pareto := 
ResolveConcatOne_pareto: ∀ {α : Type} {F : Factory α} {d : Doc} {m : Meas} {i : ℕ} {msr : List Meas} {h_non_empty : msr ≠ []},
  ResolveConcatOne F d m i (MeasureSet.set msr h_non_empty) → pareto F msr
ResolveConcatOne_pareto 
h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)
h_print
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms h_non_empty) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms h_non_empty) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truesimp [
MeasureSet.union: {α : Type} → Factory α → MeasureSet → MeasureSet → MeasureSet
MeasureSet.union]
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

¬merge F (ms✝, ms) = [] ∧ ∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = true 
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms h_non_empty) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueconstructor
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

left
¬merge F (ms✝, ms) = []
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

right
∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms h_non_empty) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecase left => 
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

¬merge F (ms✝, ms) = []apply 
merge_not_empty: ∀ {α : Type} {ms₁ ms₂ : List Meas} {F : Factory α}, ms₁ ≠ [] ∨ ms₂ ≠ [] → merge F (ms₁, ms₂) ≠ []
merge_not_empty
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

h
ms✝ ≠ [] ∨ ms ≠ []
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

¬merge F (ms✝, ms) = []simp [*]
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

∃ ms_1 h,
  MeasureSet.union F (MeasureSet.set ms✝ h✝) (MeasureSet.set ms h_non_empty) = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecase right => 
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = truelet ⟨
m_better: Meas
m_better, 
h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
h_better⟩ := 
h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
h₂
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = truehave 
h_pareto': ?m.195143
h_pareto' := 
ResolveConcat_pareto: ∀ {α : Type} {F : Factory α} {ms : List Meas} {d : Doc} {i : ℕ} {msr : List Meas} {h_non_empty : msr ≠ []},
  ResolveConcat F ms d i (MeasureSet.set msr h_non_empty) → pareto F msr
ResolveConcat_pareto 
h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)
h_rest
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = truehave 
h_pareto: ?m.195162
h_pareto := 
ResolveConcatOne_pareto: ∀ {α : Type} {F : Factory α} {d : Doc} {m : Meas} {i : ℕ} {msr : List Meas} {h_non_empty : msr ≠ []},
  ResolveConcatOne F d m i (MeasureSet.set msr h_non_empty) → pareto F msr
ResolveConcatOne_pareto 
h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)
h_print
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto✝: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

h_pareto: pareto F ms✝

∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = truehave := 
merge_dom₂: ∀ {α : Type} {F : Factory α} {ms₁ ms₂ : List Meas} {m : Meas},
  pareto F ms₁ → pareto F ms₂ → m ∈ ms₂ → ∃ m_better, m_better ∈ merge F (ms₁, ms₂) ∧ dominates F m_better m = true
merge_dom₂ 
h_pareto: ?m.195162
h_pareto 
h_pareto': ?m.195143
h_pareto' (
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto✝: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

h_pareto: pareto F ms✝

∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueby
Goals accomplished! 🐙 
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto✝: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

h_pareto: pareto F ms✝

?m.195180 ∈ ms{
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto✝: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

h_pareto: pareto F ms✝

?m.195180 ∈ ms
            
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto✝: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

h_pareto: pareto F ms✝

?m.195180 ∈ msexact 
h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
h_better.
left: ∀ {a b : Prop}, a ∧ b → a
left
Goals accomplished! 🐙
          }
Goals accomplished! 🐙)
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto✝: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

h_pareto: pareto F ms✝

this: ∃ m_better_1, m_better_1 ∈ merge F (ms✝, ms) ∧ dominates F m_better_1 m_better = true

∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = truelet ⟨
mm: Meas
mm, 
hh: mm ∈ merge F (ms✝, ms) ∧ dominates F mm m_better = true
hh⟩ := 
this: ?m.195175
this
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto✝: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

h_pareto: pareto F ms✝

this: ∃ m_better_1, m_better_1 ∈ merge F (ms✝, ms) ∧ dominates F m_better_1 m_better = true

mm: Meas

hh: mm ∈ merge F (ms✝, ms) ∧ dominates F mm m_better = true

∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueexists 
mm: Meas
mm
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto✝: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

h_pareto: pareto F ms✝

this: ∃ m_better_1, m_better_1 ∈ merge F (ms✝, ms) ∧ dominates F m_better_1 m_better = true

mm: Meas

hh: mm ∈ merge F (ms✝, ms) ∧ dominates F mm m_better = true

mm ∈ merge F (ms✝, ms) ∧ dominates F mm (Meas.concat F m₁ m₂) = true
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = truesimp [
hh: mm ∈ merge F (ms✝, ms) ∧ dominates F mm m_better = true
hh]
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto✝: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

h_pareto: pareto F ms✝

this: ∃ m_better_1, m_better_1 ∈ merge F (ms✝, ms) ∧ dominates F m_better_1 m_better = true

mm: Meas

hh: mm ∈ merge F (ms✝, ms) ∧ dominates F mm m_better = true

dominates F mm (Meas.concat F m₁ m₂) = true
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueapply 
dominates_trans: ∀ {α : Type} {m₁ m₂ m₃ : Meas} {F : Factory α},
  dominates F m₁ m₂ = true → dominates F m₂ m₃ = true → dominates F m₁ m₃ = true
dominates_trans
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto✝: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

h_pareto: pareto F ms✝

this: ∃ m_better_1, m_better_1 ∈ merge F (ms✝, ms) ∧ dominates F m_better_1 m_better = true

mm: Meas

hh: mm ∈ merge F (ms✝, ms) ∧ dominates F mm m_better = true

h
dominates F mm ?m₂ = true
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto✝: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

h_pareto: pareto F ms✝

this: ∃ m_better_1, m_better_1 ∈ merge F (ms✝, ms) ∧ dominates F m_better_1 m_better = true

mm: Meas

hh: mm ∈ merge F (ms✝, ms) ∧ dominates F mm m_better = true

h'
dominates F ?m₂ (Meas.concat F m₁ m₂) = true
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto✝: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

h_pareto: pareto F ms✝

this: ∃ m_better_1, m_better_1 ∈ merge F (ms✝, ms) ∧ dominates F m_better_1 m_better = true

mm: Meas

hh: mm ∈ merge F (ms✝, ms) ∧ dominates F mm m_better = true

m₂
Meas 
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = true. 
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto✝: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

h_pareto: pareto F ms✝

this: ∃ m_better_1, m_better_1 ∈ merge F (ms✝, ms) ∧ dominates F m_better_1 m_better = true

mm: Meas

hh: mm ∈ merge F (ms✝, ms) ∧ dominates F mm m_better = true

h
dominates F mm ?m₂ = true
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto✝: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

h_pareto: pareto F ms✝

this: ∃ m_better_1, m_better_1 ∈ merge F (ms✝, ms) ∧ dominates F m_better_1 m_better = true

mm: Meas

hh: mm ∈ merge F (ms✝, ms) ∧ dominates F mm m_better = true

h'
dominates F ?m₂ (Meas.concat F m₁ m₂) = true
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto✝: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

h_pareto: pareto F ms✝

this: ∃ m_better_1, m_better_1 ∈ merge F (ms✝, ms) ∧ dominates F m_better_1 m_better = true

mm: Meas

hh: mm ∈ merge F (ms✝, ms) ∧ dominates F mm m_better = true

m₂
Measexact 
hh: mm ∈ merge F (ms✝, ms) ∧ dominates F mm m_better = true
hh.
right: ∀ {a b : Prop}, a ∧ b → b
right
Goals accomplished! 🐙
          
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto: pareto F ms✝

∃ m_better, m_better ∈ merge F (ms✝, ms) ∧ dominates F m_better (Meas.concat F m₁ m₂) = true. 
α✝: Type

F: Factory α✝

d₂: Doc

i: ℕ

L₂: List Doc

d_right: Doc

m₂, m_better_left, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better_left m₁ = true

ms✝¹: List Meas

the_m: Meas

h_mem: List.Mem m_better_left ms✝¹

ms: List Meas

h_non_empty: ms ≠ []

h₂: ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_rest: ResolveConcat F ms✝¹ d₂ i (MeasureSet.set ms h_non_empty)

ms✝: List Meas

h✝: ms✝ ≠ []

h_print: ResolveConcatOne F d₂ the_m i (MeasureSet.set ms✝ h✝)

h_pareto✝: pareto F ms✝

m_better: Meas

h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true

h_pareto': pareto F ms

h_pareto: pareto F ms✝

this: ∃ m_better_1, m_better_1 ∈ merge F (ms✝, ms) ∧ dominates F m_better_1 m_better = true

mm: Meas

hh: mm ∈ merge F (ms✝, ms) ∧ dominates F mm m_better = true

h'
dominates F m_better (Meas.concat F m₁ m₂) = trueexact 
h_better: m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
h_better.
right: ∀ {a b : Prop}, a ∧ b → b
right
Goals accomplished! 🐙

  theorem 
ResolveConcatOne_optimal: ∀ {d₂ : Doc} {L₂ : List Doc} {d_right : Doc} {α : Type} {F : Factory α} {m_better : Meas} {i : ℕ} {ml : MeasureSet}
  {m₂ m₁ : Meas},
  Widen d₂ L₂ →
    d_right ∈ L₂ →
      ResolveConcatOne F d₂ m_better i ml →
        MeasRender F d_right m₁.last i m₂ →
          m₁.x ≤ F.W ∧ m₂.x ≤ F.W →
            m₁.y ≤ F.W ∧ m₂.y ≤ F.W →
              dominates F m_better m₁ = true →
                ∃ ms h,
                  ml = MeasureSet.set ms h ∧                     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
ResolveConcatOne_optimal
      (
h_widen: Widen d₂ L₂
h_widen: 
Widen: Doc → List Doc → Prop
Widen 
d₂: ?m.820
d₂ 
L₂: ?m.824
L₂)
      (
h_choiceless: d_right ∈ L₂
h_choiceless: 
d_right: ?m.845
d_right ∈ 
L₂: ?m.824
L₂)
      (
h_print: ResolveConcatOne F d₂ m_better i ml
h_print: 
ResolveConcatOne: {α : Type} → Factory α → Doc → Meas → ℕ → MeasureSet → Prop
ResolveConcatOne 
F: ?m.880
F 
d₂: ?m.820
d₂ 
m_better: ?m.914
m_better 
i: ?m.948
i 
ml: ?m.981
ml)
      (
h_render: MeasRender F d_right ?m.1127 i m₂
h_render: 
MeasRender: {α : Type} → Factory α → Doc → ℕ → ℕ → Meas → Prop
MeasRender 
F: ?m.880
F 
d_right: ?m.845
d_right 
m₁: ?m.1092
m₁
m₁.last: ℕ
.
last: {α : Type} → Meas → ℕ
last 
i: ?m.948
i 
m₂: ?m.1018
m₂)
      (
h_x: unknown metavariable '?_uniq.1057'
h_x: 
m₁: ?m.1092
m₁
m₁.x: unknown metavariable '?_uniq.1057'
.
x: {α : Type} → Meas → ℕ
x ≤ 
F: ?m.880
F.
W: {α : Type} → Factory α → ℕ
W ∧ 
m₂: ?m.1018
m₂.
x: {α : Type} → Meas → ℕ
x ≤ 
F: ?m.880
F.
W: {α : Type} → Factory α → ℕ
W)
      (
h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W
h_y: 
m₁: ?m.1092
m₁
m₁.y: unknown metavariable '?_uniq.1076'
.
y: {α : Type} → Meas → ℕ
y ≤ 
F: ?m.880
F.
W: {α : Type} → Factory α → ℕ
W ∧ 
m₂: ?m.1018
m₂.
y: {α : Type} → Meas → ℕ
y ≤ 
F: ?m.880
F.
W: {α : Type} → Factory α → ℕ
W)
      (
h_dom: dominates F m_better m₁ = true
h_dom: 
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates 
F: ?m.880
F 
m_better: ?m.914
m_better 
m₁: ?m.1092
m₁) :
         ∃ 
ms: ?m.1184
ms 
h: ?m.1189
h, 
ml: ?m.981
ml = 
MeasureSet.set: {α : Type} → (ms : List Meas) → ms ≠ [] → MeasureSet
MeasureSet.set 
ms: ?m.1184
ms 
h: ?m.1189
h ∧ ∃ 
m_better: ?m.1224
m_better, 
m_better: ?m.1224
m_better ∈ 
ms: ?m.1184
ms ∧ 
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates 
F: ?m.880
F 
m_better: ?m.1224
m_better (
Meas.concat: {α : Type} → Factory α → Meas → Meas → Meas
Meas.concat 
F: ?m.880
F 
m₁: ?m.1092
m₁ 
m₂: ?m.1018
m₂) := by
Goals accomplished! 🐙 
    
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truehave 
h_is_choiceless: ?m.201386
h_is_choiceless := 
Widen_choiceless: ∀ {d : Doc} {D : List Doc} {d_choiceless : Doc}, Widen d D → d_choiceless ∈ D → Choiceless d_choiceless
Widen_choiceless 
h_widen: Widen d₂ L₂
h_widen 
h_choiceless: d_right ∈ L₂
h_choiceless
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
    
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truelet ⟨
m_result_better: Meas
m_result_better, 
h_render_better: MeasRender F d_right m_better.last i m_result_better
h_render_better⟩ := 
MeasRender_total: ∀ {α : Type} (F : Factory α) (d : Doc) (c i : ℕ), Choiceless d → ∃ m, MeasRender F d c i m
MeasRender_total 
F: Factory α✝
F 
d_right: Doc
d_right 
m_better: Meas
m_better.
last: {α : Type} → Meas → ℕ
last 
i: ℕ
i 
h_is_choiceless: ?m.201386
h_is_choiceless
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true 
    
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truehave 
h_dom_better: ?m.201504
h_dom_better := 
MeasRender_dom_monotonic: ∀ {α : Type} {d : Doc} {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas} {F : Factory α},
  MeasRender F d c i m₁ → MeasRender F d c' i' m₂ → c ≤ c' → i ≤ i' → dominates F m₁ m₂ = true
MeasRender_dom_monotonic 
h_render_better: MeasRender F d_right m_better.last i m_result_better
h_render_better 
h_render: MeasRender F d_right m₁.last i m₂
h_render (
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueby
Goals accomplished! 🐙 
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

m_better.last ≤ m₁.last{
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

m_better.last ≤ m₁.last
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

m_better.last ≤ m₁.lastsimp [
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates] at 
h_dom: dominates F m_better m₁ = true
h_dom
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

m_better.last ≤ m₁.last
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

m_better.last ≤ m₁.lastsimp [
h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true
h_dom]
Goals accomplished! 🐙
    }
Goals accomplished! 🐙) (
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueby
Goals accomplished! 🐙 
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

i ≤ isimp
Goals accomplished! 🐙)
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
    
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truehave 
h_dom_good: ?m.202173
h_dom_good := 
MeasRender_dom_is_good: ∀ {α : Type} {d : Doc} {c i : ℕ} {m₁ : Meas} {c' i' : ℕ} {m₂ : Meas} {F : Factory α},
  MeasRender F d c i m₁ → MeasRender F d c' i' m₂ → c ≤ c' → i ≤ i' → m₂.x ≤ F.W → m₂.y ≤ F.W → m₁.x ≤ F.W ∧ m₁.y ≤ F.W
MeasRender_dom_is_good 
h_render_better: MeasRender F d_right m_better.last i m_result_better
h_render_better 
h_render: MeasRender F d_right m₁.last i m₂
h_render (
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueby
Goals accomplished! 🐙 
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

m_better.last ≤ m₁.last{
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

m_better.last ≤ m₁.last
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

m_better.last ≤ m₁.lastsimp [
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates] at 
h_dom: dominates F m_better m₁ = true
h_dom
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

m_better.last ≤ m₁.last
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

m_better.last ≤ m₁.lastsimp [
h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true
h_dom]
Goals accomplished! 🐙
    }
Goals accomplished! 🐙) (
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueby
Goals accomplished! 🐙 
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

i ≤ isimp
Goals accomplished! 🐙) (
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueby
Goals accomplished! 🐙 
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

m₂.x ≤ F.Wsimp [
h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W
h_x]
Goals accomplished! 🐙) (
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueby
Goals accomplished! 🐙 
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

m₂.y ≤ F.Wsimp [
h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W
h_y]
Goals accomplished! 🐙)
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
    
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecases 
h_print: ResolveConcatOne F d₂ m_better i ml
h_print
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

m'✝: Meas

h✝: Resolve F d₂ m_better.last i (MeasureSet.tainted m'✝)

tainted
∃ ms h,
  MeasureSet.tainted (Meas.concat F m_better m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms✝: List Meas

h_non_empty✝: ms✝ ≠ []

h✝: Resolve F d₂ m_better.last i (MeasureSet.set ms✝ h_non_empty✝)

set
∃ ms h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms✝))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms✝) ≠ []) =       MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
    
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecase tainted 
h_print: Resolve F d₂ m_better.last i (MeasureSet.tainted m'✝)
h_print => 
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

m'✝: Meas

h_print: Resolve F d₂ m_better.last i (MeasureSet.tainted m'✝)

∃ ms h,
  MeasureSet.tainted (Meas.concat F m_better m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truehave := 
Resolve_optimal: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ml : MeasureSet} {D : List Doc} {d_choiceless : Doc} {m : Meas},
  Resolve F d c i ml →
    Widen d D →
      d_choiceless ∈ D →
        MeasRender F d_choiceless c i m →
          m.y ≤ F.W →
            m.x ≤ F.W → ∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
Resolve_optimal 
h_print: Resolve F d₂ m_better.last i (MeasureSet.tainted m'✝)
h_print 
h_widen: Widen d₂ L₂
h_widen 
h_choiceless: d_right ∈ L₂
h_choiceless (
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

m'✝: Meas

h_print: Resolve F d₂ m_better.last i (MeasureSet.tainted m'✝)

∃ ms h,
  MeasureSet.tainted (Meas.concat F m_better m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueby
Goals accomplished! 🐙 
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

m'✝: Meas

h_print: Resolve F d₂ m_better.last i (MeasureSet.tainted m'✝)

MeasRender F d_right m_better.last i m_result_betterassumption
Goals accomplished! 🐙) 
h_dom_good: ?m.202173
h_dom_good.
right: ∀ {a b : Prop}, a ∧ b → b
right 
h_dom_good: ?m.202173
h_dom_good.
left: ∀ {a b : Prop}, a ∧ b → a
left
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

m'✝: Meas

h_print: Resolve F d₂ m_better.last i (MeasureSet.tainted m'✝)

this: ∃ ms h,
  MeasureSet.tainted m'✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m_result_better = true

∃ ms h,
  MeasureSet.tainted (Meas.concat F m_better m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true 
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

m'✝: Meas

h_print: Resolve F d₂ m_better.last i (MeasureSet.tainted m'✝)

∃ ms h,
  MeasureSet.tainted (Meas.concat F m_better m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truelet ⟨
_: List Meas
_, 
_: w✝¹ ≠ []
_, _, _⟩ := 
this: ?m.203167
this
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

m'✝: Meas

h_print: Resolve F d₂ m_better.last i (MeasureSet.tainted m'✝)

this: ∃ ms h,
  MeasureSet.tainted m'✝ = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m_result_better = true

w✝¹: List Meas

w✝: w✝¹ ≠ []

left✝: MeasureSet.tainted m'✝ = MeasureSet.set w✝¹ w✝

right✝: ∃ m_better, m_better ∈ w✝¹ ∧ dominates F m_better m_result_better = true

∃ ms h,
  MeasureSet.tainted (Meas.concat F m_better m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

m'✝: Meas

h_print: Resolve F d₂ m_better.last i (MeasureSet.tainted m'✝)

∃ ms h,
  MeasureSet.tainted (Meas.concat F m_better m'✝) = MeasureSet.set ms h ∧     ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecontradiction
Goals accomplished! 🐙
    
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

ml: MeasureSet

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_print: ResolveConcatOne F d₂ m_better i ml

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecase set 
ms: List Meas
ms _ 
h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)
h_print => 
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truehave := 
Resolve_optimal: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ml : MeasureSet} {D : List Doc} {d_choiceless : Doc} {m : Meas},
  Resolve F d c i ml →
    Widen d D →
      d_choiceless ∈ D →
        MeasRender F d_choiceless c i m →
          m.y ≤ F.W →
            m.x ≤ F.W → ∃ ms h, ml = MeasureSet.set ms h ∧ ∃ m_better, m_better ∈ ms ∧ dominates F m_better m = true
Resolve_optimal 
h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)
h_print 
h_widen: Widen d₂ L₂
h_widen 
h_choiceless: d_right ∈ L₂
h_choiceless (
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueby
Goals accomplished! 🐙 
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

MeasRender F d_right m_better.last i m_result_betterassumption
Goals accomplished! 🐙) 
h_dom_good: ?m.202173
h_dom_good.
right: ∀ {a b : Prop}, a ∧ b → b
right 
h_dom_good: ?m.202173
h_dom_good.
left: ∀ {a b : Prop}, a ∧ b → a
left
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true 
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truelet ⟨
_: List Meas
_, 
h: w✝ ≠ []
h, 
h_left: MeasureSet.set ms h_non_empty✝ = MeasureSet.set w✝ h
h_left, 
m_better_right: Meas
m_better_right, 
h_better_right: m_better_right ∈ w✝ ∧ dominates F m_better_right m_result_better = true
h_better_right⟩ := 
this: ?m.206437
this
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

w✝: List Meas

h: w✝ ≠ []

h_left: MeasureSet.set ms h_non_empty✝ = MeasureSet.set w✝ h

m_better_right: Meas

h_better_right: m_better_right ∈ w✝ ∧ dominates F m_better_right m_result_better = true

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecases 
h_left: MeasureSet.set ms h_non_empty✝ = MeasureSet.set w✝ h
h_left
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

m_better_right: Meas

h: ms ≠ []

h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true

refl
∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = true
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueexists 
dedup: {α : Type} → Factory α → List Meas → List Meas
dedup 
F: Factory α✝
F (
ms: List Meas
ms.
map: {α : Type ?u.206851} → {β : Type ?u.206850} → (α → β) → List α → List β
map (fun 
m': ?m.206859
m' => 
Meas.concat: {α : Type} → Factory α → Meas → Meas → Meas
Meas.concat 
F: Factory α✝
F 
m_better: Meas
m_better 
m': ?m.206859
m')), (
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

m_better_right: Meas

h: ms ≠ []

h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true

refl
∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueby
Goals accomplished! 🐙 
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

m_better_right: Meas

h: ms ≠ []

h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true

dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []{
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

m_better_right: Meas

h: ms ≠ []

h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true

dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []
        
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

m_better_right: Meas

h: ms ≠ []

h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true

dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []apply 
dedup_not_empty: ∀ {α : Type} {ms : List Meas} {F : Factory α}, ms ≠ [] → dedup F ms ≠ []
dedup_not_empty
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

m_better_right: Meas

h: ms ≠ []

h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true

h
List.map (fun m' => Meas.concat F m_better m') ms ≠ []
        
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

m_better_right: Meas

h: ms ≠ []

h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true

dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []simp [
h: ms ≠ []
h]
Goals accomplished! 🐙
      }
Goals accomplished! 🐙)
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

m_better_right: Meas

h: ms ≠ []

h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true

refl
MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
      (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =     MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
      (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) ∧   ∃ m_better_1,
    m_better_1 ∈ dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ∧       dominates F m_better_1 (Meas.concat F m₁ m₂) = true
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truesimp
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

m_better_right: Meas

h: ms ≠ []

h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true

refl
∃ m_better_1,
  m_better_1 ∈ dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ∧     dominates F m_better_1 (Meas.concat F m₁ m₂) = true
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truehave 
h_pareto: ?m.217184
h_pareto := 
Resolve_pareto: ∀ {α : Type} {F : Factory α} {d : Doc} {c i : ℕ} {ms : List Meas} {h_non_empty : ms ≠ []},
  Resolve F d c i (MeasureSet.set ms h_non_empty) → pareto F ms
Resolve_pareto 
h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)
h_print
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

m_better_right: Meas

h: ms ≠ []

h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true

h_pareto: pareto F ms

refl
∃ m_better_1,
  m_better_1 ∈ dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ∧     dominates F m_better_1 (Meas.concat F m₁ m₂) = true
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truehave 
h_cost: ?m.217200
h_cost := 
cost_increasing_non_strict_concat: ∀ {α : Type} {F : Factory α} {ms : List Meas} (m : Meas),
  cost_increasing F ms → cost_increasing_non_strict F (List.map (fun m' => Meas.concat F m m') ms)
cost_increasing_non_strict_concat 
m_better: Meas
m_better 
h_pareto: ?m.217184
h_pareto.
right: ∀ {a b : Prop}, a ∧ b → b
right
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

m_better_right: Meas

h: ms ≠ []

h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true

h_pareto: pareto F ms

h_cost: cost_increasing_non_strict F (List.map (fun m' => Meas.concat F m_better m') ms)

refl
∃ m_better_1,
  m_better_1 ∈ dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ∧     dominates F m_better_1 (Meas.concat F m₁ m₂) = true
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truehave 
h_last: ?m.217226
h_last := 
last_decreasing_concat: ∀ {α : Type} {ms : List Meas} (F : Factory α) (m : Meas),
  last_decreasing ms → last_decreasing (List.map (fun m' => Meas.concat F m m') ms)
last_decreasing_concat 
F: Factory α✝
F 
m_better: Meas
m_better 
h_pareto: ?m.217184
h_pareto.
left: ∀ {a b : Prop}, a ∧ b → a
left
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

m_better_right: Meas

h: ms ≠ []

h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true

h_pareto: pareto F ms

h_cost: cost_increasing_non_strict F (List.map (fun m' => Meas.concat F m_better m') ms)

h_last: last_decreasing (List.map (fun m' => Meas.concat F m_better m') ms)

refl
∃ m_better_1,
  m_better_1 ∈ dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ∧     dominates F m_better_1 (Meas.concat F m₁ m₂) = true
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truelet ⟨
m_ult: Meas
m_ult, 
h_mem_ult: m_ult ∈ dedup F (List.map (fun m' => Meas.concat F m_better m') ms)
h_mem_ult, 
h_dom_ult: dominates F m_ult ((fun m' => Meas.concat F m_better m') m_better_right) = true
h_dom_ult⟩ := 
dedup_dom: ∀ {α : Type} {m : Meas} {ms : List Meas} {F : Factory α},
  m ∈ ms →
    last_decreasing ms →
      cost_increasing_non_strict F ms → ∃ m_better, m_better ∈ dedup F ms ∧ dominates F m_better m = true
dedup_dom 
        (
List.mem_map_of_mem: ∀ {α : Type ?u.217250} {β : Type ?u.217251} {a : α} {l : List α} (f : α → β), a ∈ l → f a ∈ List.map f l
List.mem_map_of_mem (fun 
m': ?m.217257
m' => 
Meas.concat: {α : Type} → Factory α → Meas → Meas → Meas
Meas.concat 
F: Factory α✝
F 
m_better: Meas
m_better 
m': ?m.217257
m')
        
h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true
h_better_right.
left: ∀ {a b : Prop}, a ∧ b → a
left) 
h_last: ?m.217226
h_last 
h_cost: ?m.217200
h_cost
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

m_better_right: Meas

h: ms ≠ []

h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true

h_pareto: pareto F ms

h_cost: cost_increasing_non_strict F (List.map (fun m' => Meas.concat F m_better m') ms)

h_last: last_decreasing (List.map (fun m' => Meas.concat F m_better m') ms)

m_ult: Meas

h_mem_ult: m_ult ∈ dedup F (List.map (fun m' => Meas.concat F m_better m') ms)

h_dom_ult: dominates F m_ult ((fun m' => Meas.concat F m_better m') m_better_right) = true

refl
∃ m_better_1,
  m_better_1 ∈ dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ∧     dominates F m_better_1 (Meas.concat F m₁ m₂) = true
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueexists 
m_ult: Meas
m_ult
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

m_better_right: Meas

h: ms ≠ []

h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true

h_pareto: pareto F ms

h_cost: cost_increasing_non_strict F (List.map (fun m' => Meas.concat F m_better m') ms)

h_last: last_decreasing (List.map (fun m' => Meas.concat F m_better m') ms)

m_ult: Meas

h_mem_ult: m_ult ∈ dedup F (List.map (fun m' => Meas.concat F m_better m') ms)

h_dom_ult: dominates F m_ult ((fun m' => Meas.concat F m_better m') m_better_right) = true

refl
m_ult ∈ dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ∧ dominates F m_ult (Meas.concat F m₁ m₂) = true 
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truesimp [
h_mem_ult: m_ult ∈ dedup F (List.map (fun m' => Meas.concat F m_better m') ms)
h_mem_ult]
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

this: ∃ ms_1 h,
  MeasureSet.set ms h_non_empty✝ = MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better m_result_better = true

m_better_right: Meas

h: ms ≠ []

h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true

h_pareto: pareto F ms

h_cost: cost_increasing_non_strict F (List.map (fun m' => Meas.concat F m_better m') ms)

h_last: last_decreasing (List.map (fun m' => Meas.concat F m_better m') ms)

m_ult: Meas

h_mem_ult: m_ult ∈ dedup F (List.map (fun m' => Meas.concat F m_better m') ms)

h_dom_ult: dominates F m_ult ((fun m' => Meas.concat F m_better m') m_better_right) = true

refl
dominates F m_ult (Meas.concat F m₁ m₂) = true
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueclear * - 
h_dom_ult: dominates F m_ult ((fun m' => Meas.concat F m_better m') m_better_right) = true
h_dom_ult 
h_dom: dominates F m_better m₁ = true
h_dom 
h_dom_better: ?m.201504
h_dom_better 
h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true
h_better_right
α✝: Type

F: Factory α✝

m_better, m₂, m₁: Meas

h_dom: dominates F m_better m₁ = true

m_result_better: Meas

h_dom_better: dominates F m_result_better m₂ = true

ms: List Meas

m_better_right: Meas

h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true

m_ult: Meas

h_dom_ult: dominates F m_ult ((fun m' => Meas.concat F m_better m') m_better_right) = true

refl
dominates F m_ult (Meas.concat F m₁ m₂) = true
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truesimp [
dominates: {α : Type} → Factory α → Meas → Meas → Bool
dominates] at 
h_dom_ult: dominates F m_ult ((fun m' => Meas.concat F m_better m') m_better_right) = true
h_dom_ult 
h_dom: dominates F m_better m₁ = true
h_dom 
h_dom_better: ?m.201504
h_dom_better 
h_better_right: m_better_right ∈ ms ∧ dominates F m_better_right m_result_better = true
h_better_right ⊢
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

refl
m_ult.last ≤ m₂.last ∧ Factory.le F m_ult.cost (Factory.concat F m₁.cost m₂.cost) = true  
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = trueconstructor
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

refl.left
m_ult.last ≤ m₂.last
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

refl.right
Factory.le F m_ult.cost (Factory.concat F m₁.cost m₂.cost) = true 
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecase left => 
        
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

m_ult.last ≤ m₂.lasthave 
aa: ?m.230353
aa := 
h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true
h_dom_ult.
left: ∀ {a b : Prop}, a ∧ b → a
left
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: m_ult.last ≤ m_better_right.last

m_ult.last ≤ m₂.last
        
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

m_ult.last ≤ m₂.lasthave 
bb: ?m.230361
bb := 
h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true
h_better_right.
right: ∀ {a b : Prop}, a ∧ b → b
right.
left: ∀ {a b : Prop}, a ∧ b → a
left
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: m_ult.last ≤ m_better_right.last

bb: m_better_right.last ≤ m_result_better.last

m_ult.last ≤ m₂.last 
        
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

m_ult.last ≤ m₂.lasthave 
cc: ?m.230371
cc := 
h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true
h_dom_better.
left: ∀ {a b : Prop}, a ∧ b → a
left
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: m_ult.last ≤ m_better_right.last

bb: m_better_right.last ≤ m_result_better.last

cc: m_result_better.last ≤ m₂.last

m_ult.last ≤ m₂.last
        
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

m_ult.last ≤ m₂.lastclear * - 
aa: ?m.230353
aa 
bb: ?m.230361
bb 
cc: ?m.230371
cc
α✝: Type

m₂, m_result_better, m_better_right, m_ult: Meas

aa: m_ult.last ≤ m_better_right.last

bb: m_better_right.last ≤ m_result_better.last

cc: m_result_better.last ≤ m₂.last

m_ult.last ≤ m₂.last
        
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

m_ult.last ≤ m₂.lastlinarith
Goals accomplished! 🐙 
      
d₂: Doc

L₂: List Doc

d_right: Doc

α✝: Type

F: Factory α✝

m_better: Meas

i: ℕ

m₂, m₁: Meas

h_widen: Widen d₂ L₂

h_choiceless: d_right ∈ L₂

h_render: MeasRender F d_right m₁.last i m₂

h_x: m₁.x ≤ F.W ∧ m₂.x ≤ F.W

h_y: m₁.y ≤ F.W ∧ m₂.y ≤ F.W

h_dom: dominates F m_better m₁ = true

h_is_choiceless: Choiceless d_right

m_result_better: Meas

h_render_better: MeasRender F d_right m_better.last i m_result_better

h_dom_better: dominates F m_result_better m₂ = true

h_dom_good: m_result_better.x ≤ F.W ∧ m_result_better.y ≤ F.W

ms: List Meas

h_non_empty✝: ms ≠ []

h_print: Resolve F d₂ m_better.last i (MeasureSet.set ms h_non_empty✝)

∃ ms_1 h,
  MeasureSet.set (dedup F (List.map (fun m' => Meas.concat F m_better m') ms))
        (_ : dedup F (List.map (fun m' => Meas.concat F m_better m') ms) ≠ []) =       MeasureSet.set ms_1 h ∧     ∃ m_better, m_better ∈ ms_1 ∧ dominates F m_better (Meas.concat F m₁ m₂) = truecase right => 
        
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

Factory.le F m_ult.cost (Factory.concat F m₁.cost m₂.cost) = truehave 
aa: ?m.232150
aa := 
h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true
h_dom_ult.
right: ∀ {a b : Prop}, a ∧ b → b
right
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

Factory.le F m_ult.cost (Factory.concat F m₁.cost m₂.cost) = true
        
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

Factory.le F m_ult.cost (Factory.concat F m₁.cost m₂.cost) = truehave 
bb: ?m.232160
bb := 
h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true
h_better_right.
right: ∀ {a b : Prop}, a ∧ b → b
right.
right: ∀ {a b : Prop}, a ∧ b → b
right
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

Factory.le F m_ult.cost (Factory.concat F m₁.cost m₂.cost) = true
        
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

Factory.le F m_ult.cost (Factory.concat F m₁.cost m₂.cost) = truehave 
cc: ?m.232170
cc := 
h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true
h_dom_better.
right: ∀ {a b : Prop}, a ∧ b → b
right
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

Factory.le F m_ult.cost (Factory.concat F m₁.cost m₂.cost) = true
        
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

Factory.le F m_ult.cost (Factory.concat F m₁.cost m₂.cost) = truehave 
dd: ?m.232178
dd := 
h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true
h_dom.
right: ∀ {a b : Prop}, a ∧ b → b
right
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

Factory.le F m_ult.cost (Factory.concat F m₁.cost m₂.cost) = true
        
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

Factory.le F m_ult.cost (Factory.concat F m₁.cost m₂.cost) = trueapply 
Factory.le_trans: ∀ {α : Type} (self : Factory α) {c₁ c₂ c₃ : α},
  Factory.le self c₁ c₂ = true → Factory.le self c₂ c₃ = true → Factory.le self c₁ c₃ = true
Factory.le_trans
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a
Factory.le F m_ult.cost ?c₂ = true
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a
Factory.le F ?c₂ (Factory.concat F m₁.cost m₂.cost) = true
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

c₂
α✝ 
        
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

Factory.le F m_ult.cost (Factory.concat F m₁.cost m₂.cost) = true. 
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a
Factory.le F m_ult.cost ?c₂ = true
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a
Factory.le F ?c₂ (Factory.concat F m₁.cost m₂.cost) = true
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

c₂
α✝assumption
Goals accomplished! 🐙
        
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

Factory.le F m_ult.cost (Factory.concat F m₁.cost m₂.cost) = true. 
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a
Factory.le F (Factory.concat F m_better.cost m_better_right.cost) (Factory.concat F m₁.cost m₂.cost) = trueapply 
Factory.concat_monotonic: ∀ {α : Type} (self : Factory α) {cost₁ cost₂ cost₃ cost₄ : α},
  Factory.le self cost₁ cost₂ = true →
    Factory.le self cost₃ cost₄ = true →
      Factory.le self (Factory.concat self cost₁ cost₃) (Factory.concat self cost₂ cost₄) = true
Factory.concat_monotonic
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a.a
Factory.le F m_better.cost m₁.cost = true
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a.a
Factory.le F m_better_right.cost m₂.cost = true 
          
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a
Factory.le F (Factory.concat F m_better.cost m_better_right.cost) (Factory.concat F m₁.cost m₂.cost) = true. 
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a.a
Factory.le F m_better.cost m₁.cost = true
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a.a
Factory.le F m_better_right.cost m₂.cost = trueapply 
dd: ?m.232178
dd
Goals accomplished! 🐙
          
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a
Factory.le F (Factory.concat F m_better.cost m_better_right.cost) (Factory.concat F m₁.cost m₂.cost) = true. 
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a.a
Factory.le F m_better_right.cost m₂.cost = trueapply 
Factory.le_trans: ∀ {α : Type} (self : Factory α) {c₁ c₂ c₃ : α},
  Factory.le self c₁ c₂ = true → Factory.le self c₂ c₃ = true → Factory.le self c₁ c₃ = true
Factory.le_trans
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a.a.a
Factory.le F m_better_right.cost ?a.a.c₂✝ = true
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a.a.a
Factory.le F ?a.a.c₂✝ m₂.cost = true
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a.a.c₂
α✝ 
            
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a.a
Factory.le F m_better_right.cost m₂.cost = true. 
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a.a.a
Factory.le F m_better_right.cost ?a.a.c₂✝ = true
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a.a.a
Factory.le F ?a.a.c₂✝ m₂.cost = true
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a.a.c₂
α✝assumption
Goals accomplished! 🐙 
            
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a.a
Factory.le F m_better_right.cost m₂.cost = true. 
α✝: Type

F: Factory α✝

m_better, m₂, m₁, m_result_better: Meas

ms: List Meas

m_better_right, m_ult: Meas

h_dom_ult: m_ult.last ≤ m_better_right.last ∧ Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

h_dom: m_better.last ≤ m₁.last ∧ Factory.le F m_better.cost m₁.cost = true

h_dom_better: m_result_better.last ≤ m₂.last ∧ Factory.le F m_result_better.cost m₂.cost = true

h_better_right: m_better_right ∈ ms ∧   m_better_right.last ≤ m_result_better.last ∧ Factory.le F m_better_right.cost m_result_better.cost = true

aa: Factory.le F m_ult.cost (Factory.concat F m_better.cost m_better_right.cost) = true

bb: Factory.le F m_better_right.cost m_result_better.cost = true

cc: Factory.le F m_result_better.cost m₂.cost = true

dd: Factory.le F m_better.cost m₁.cost = true

a.a.a
Factory.le F m_result_better.cost m₂.cost = trueassumption
Goals accomplished! 🐙
end
termination_by 
  Resolve_optimal => (
d: Doc
d.
size: Doc → ℕ
size, 
0: ?m.247913
0, 
0: ?m.247924
0)
  ResolveConcat_optimal => (
d₂: Doc
d₂.
size: Doc → ℕ
size, 
2: ?m.248330
2, 
ms: List Meas
ms.
length: {α : Type ?u.248339} → List α → ℕ
length)
  ResolveConcatOne_optimal => (
d₂: Doc
d₂.
size: Doc → ℕ
size, 
1: ?m.248660
1, 
0: ?m.248667
0)